The Bethe lattice spin glass revisited

Abstract

So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a replica symmetry breaking solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Using the cavity method, we propose a general non perturbative solution of the Bethe lattice spin glass problem at a level of approximation which is equivalent to a one step replica symmetry breaking solution. The results compare well with numerical simulations. The method can be used for many finite connectivity problems appearing in combinatorial optimization.

23 pages, 6 figures

Cited by in corpus (527)

• ARACNE: An Algorithm for the Reconstruction of Gene Regulatory Networks in a Mammalian Cellular Context
• Critical phenomena in complex networks
• Vital nodes identification in complex networks
• Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications
• Control Principles of Complex Networks
• Gibbs States and the Set of Solutions of Random Constraint Satisfaction Problems
• The random K-satisfiability problem: from an analytic solution to an efficient algorithm
• Statistical physics of inference: Thresholds and algorithms
• Phase transition in the detection of modules in sparse networks
• Phase Transitions in the Coloring of Random Graphs
• Network dismantling
• Lattice Glass Models
• Coloring random graphs
• Scalable detection of statistically significant communities and hierarchies, using message-passing for modularity
• Survey propagation: an algorithm for satisfiability
• Jamming versus Glass Transitions
• Network Controllability Is Determined by the Density of Low In-Degree and Out-Degree Nodes
• The number of matchings in random graphs
• Quantum Graphical Models and Belief Propagation
• Glass models on Bethe lattices
• Cavity Approach to the Spectral Density of Sparse Symmetric Random Matrices
• Non-ergodic phases in strongly disordered random regular graphs
• Cluster Variation Method in Statistical Physics and Probabilistic Graphical Models
• Survey Propagation as local equilibrium equations
• Clusters of solutions and replica symmetry breaking in random k-satisfiability
• Hiding Quiet Solutions in Random Constraint Satisfaction Problems
• Spectra of Sparse Random Matrices
• A ferromagnet with a glass transition
• Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
• Instability of one-step replica-symmetry-broken phase in satisfiability problems
• Cayley Trees and Bethe Lattices, a concise analysis for mathematicians and physicists
• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
• Polynomial iterative algorithms for coloring and analyzing random graphs
• The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
• Phase Transitions in Semidefinite Relaxations
• Exact solutions for diluted spin glasses and optimization problems
• On the freezing of variables in random constraint satisfaction problems
• Hiding solutions in random satisfiability problems: A statistical mechanics approach
• On the dynamics of the glass transition on Bethe lattices
• First-order transitions and the performance of quantum algorithms in random optimization problems
• Superconductor-Insulator transition and energy localization
• Diluted one-dimensional spin glasses with power law decaying interactions
• On the cooling-schedule dependence of the dynamics of mean-field glasses
• Extremal Optimization for Sherrington-Kirkpatrick Spin Glasses
• Control of Multilayer Networks
• Information-theoretic thresholds from the cavity method
• Replica bounds for diluted non-Poissonian spin systems
• Spin glass approach to the feedback vertex set problem
• The Bethe approximation for solving the inverse Ising problem: a comparison with other inference methods
• Energy transport in strongly disordered superconductors and magnets
• The Dynamic Phase Transition for Decoding Algorithms
• How to Compute Loop Corrections to Bethe Approximation
• Cavity approach to the spectral density of non-Hermitian sparse matrices
• On the localization transition in symmetric random matrices
• Generalization of the cavity method for adiabatic evolution of Gibbs states
• Optimizing spread dynamics on graphs by message passing
• Landscape of solutions in constraint satisfaction problems
• On the path integral representation for quantum spin models and its application to the quantum cavity method and to Monte Carlo simulations
• Statistical mechanics of complex neural systems and high dimensional data
• Cavity method for quantum spin glasses on the Bethe lattice
• Entropy landscape and non-Gibbs solutions in constraint satisfaction problems
• On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms
• Behavior of Ising Spin Glasses in a Magnetic Field
• Perspective: Gardner Physics in Amorphous Solids and Beyond
• Anderson transition on the Bethe lattice: an approach with real energies
• Dynamic message-passing equations for models with unidirectional dynamics
• Finding One Community in a Sparse Graph
• Extensive load in multitasking associative networks
• Spectral Theory of Sparse Non-Hermitian Random Matrices
• Elusive Glassy Phase in the Random Field Ising Model
• Replicated Transfer Matrix Analysis of Ising Spin Models on `Small World' Lattices
• Threshold values, stability analysis and high-q asymptotics for the coloring problem on random graphs
• Message passing for vertex covers
• Balance and Frustration in Signed Networks
• Locked constraint satisfaction problems
• Level statistics and localization transitions of Lévy matrices
• Following Gibbs States Adiabatically - The Energy Landscape of Mean Field Glassy Systems
• Phase transitions in semisupervised clustering of sparse networks
• Constraint satisfaction problems with isolated solutions are hard
• Computational complexity arising from degree correlations in networks
• Random Pinning Glass Transition: Hallmarks, Mean-Field Theory and Renormalization Group Analysis
• Pairs of SAT Assignment in Random Boolean Formulae
• Cavity and replica methods for the spectral density of sparse symmetric random matrices
• Large deviations of cascade processes on graphs
• Out-of-equilibrium dynamical mean-field equations for the perceptron model
• Immune networks: multi-tasking capabilities near saturation
• Statistical Mechanics of Steiner trees
• Tropical Tensor Network for Ground States of Spin Glasses
• The Cavity Approach to Parallel Dynamics of Ising Spins on a Graph
• Networking - A Statistical Physics Perspective
• The Phase Diagram of 1-in-3 Satisfiability Problem
• Cavity-based robustness analysis of interdependent networks: Influences of intranetwork and internetwork degree-degree correlations
• Emergent fractal phase in energy stratified random models
• Spin Glass in a Field: a New Zero-Temperature Fixed Point in Finite Dimensions
• Numerical Results for Ground States of Mean-Field Spin Glasses at low Connectivities
• Typology of phase transitions in Bayesian inference problems
• Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase
• Universality in Anderson localization on random graphs with varying connectivity
• Minimal contagious sets in random regular graphs
• Long Range Frustrations in a Spin Glass Model of the Vertex Cover Problem
• Potts Glass on Random Graphs
• Loop expansion around the Bethe-Peierls approximation for lattice models
• Statistical Mechanics of the Minimum Dominating Set Problem
• Glass transition in granular media
• Geometrical organization of solutions to random linear Boolean equations
• Random multi-index matching problems
• Exact solution of the Bose-Hubbard model on the Bethe lattice
• Mean-field model for the density of states of jammed soft spheres
• Quiet Planting in the Locked Constraint Satisfaction Problems
• The Valence Bond Glass phase
• Finitely connected vector spin systems with random matrix interactions
• On the number of circuits in random graphs
• Multipartite Entanglement and Frustration
• Random subcubes as a toy model for constraint satisfaction problems
• On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field
• Glassy behavior induced by geometrical frustration in a hard-core lattice gas model
• Eigenvalue Outliers of non-Hermitian Random Matrices with a Local Tree Structure
• Disorder chaos in spin glasses
• Finite-Connectivity Spin-Glass Phase Diagrams and Low Density Parity Check Codes
• Sparsely-spread CDMA - a statistical mechanics based analysis
• Large deviation function for the number of eigenvalues of sparse random graphs inside an interval
• A Lattice Model for Colloidal Gels and Glasses
• Exhaustive enumeration unveils clustering and freezing in random 3-SAT
• Statistical mechanics of the vertex-cover problem
• Analytic solution of attractor neural networks on scale-free graphs
• Dynamic mean-field and cavity methods for diluted Ising systems
• The 3-SAT problem with large number of clauses in $\infty$-replica symmetry breaking scheme
• Mean-field inference methods for neural networks
• Charting the replica symmetric phase
• Region graph partition function expansion and approximate free energy landscapes: Theory and some numerical results
• Advanced Mean Field Theory of Restricted Boltzmann Machine
• Statistical Mechanics of maximal independent sets
• Approximation schemes for the dynamics of diluted spin models: the Ising ferromagnet on a Bethe lattice
• Cavity analysis on the robustness of random networks against targeted attacks: Influences of degree-degree correlations
• Entropy landscape of solutions in the binary perceptron problem
• Predicting protein functions with message passing algorithms
• Spectra of Modular and Small-World Matrices
• Gallager error correcting codes for binary asymmetric channels
• Solving the Graph Isomorphism Problem with a Quantum Annealer
• Partition function loop series for a general graphical model: free energy corrections and message-passing equations
• Propagating beliefs in spin glass models
• Conjecture on the maximum cut and bisection width in random regular graphs
• Marginal States in Mean Field Glasses
• Critical behavior of the Anderson model on the Bethe lattice via a large-deviation approach
• Unsupervised and semi-supervised clustering by message passing: Soft-constraint affinity propagation
• Spin glass models with ferromagnetically biased couplings on the Bethe lattice: analytic solutions and numerical simulations
• Cavity approach for real variables on diluted graphs and application to synchronization in small-world lattices
• SAT-assembly: A new approach for designing self-assembling systems
• Circuits in random graphs: from local trees to global loops
• Criticality on networks with topology-dependent interactions
• The Little-Hopfield model on a Random Graph
• Dynamical replica analysis of disordered Ising spin systems on finitely connected random graphs
• Spectral density of random graphs with topological constraints
• Sparse generative modeling via parameter-reduction of Boltzmann machines: application to protein-sequence families
• Finite size corrections to disordered Ising models on Random Regular Graphs
• Statistical Mechanics of the Hyper Vertex Cover Problem
• Diluted Mean-Field Spin-Glass Models at Criticality
• An algorithm for counting circuits: application to real-world and random graphs
• A frozen glass phase in the multi-index matching problem
• Replica Cluster Variational Method
• Community Detection with and without Prior Information
• Renormalization Group Analysis of the Anderson Model on Random Regular Graphs
• The cavity method for quantum disordered systems: from transverse random field ferromagnets to directed polymers in random media
• Linear stability analysis for large dynamical systems on directed random graphs
• Statistical mechanics of unsupervised feature learning in a restricted Boltzmann machine with binary synapses
• A message-passing scheme for non-equilibrium stationary states
• Bose-Einstein condensation in quantum glasses
• Finitely coordinated models for low-temperature phases of amorphous systems
• Approximating the XY model on a random graph with a $q$-state clock model
• Universal transient behavior in large dynamical systems on networks
• Ground state of the Bethe-lattice spin glass and running time of an exact optimization algorithm
• Limits and performances of algorithms based on simulated annealing in solving sparse hard inference problems
• Belief propagation algorithm for computing correlation functions in finite-temperature quantum many-body systems on loopy graphs
• Dimensional study of the dynamical arrest in a random Lorentz gas
• Near optimal configurations in mean field disordered systems
• Stability analysis on the finite-temperature replica-symmetric and first-step replica-symmetry-broken cavity solutions of the random vertex cover problem
• When a local Hamiltonian must be frustration-free
• Heterogeneous micro-structure of percolation in sparse networks
• There are no Goldstone bosons on the Bethe lattice
• The quantum Biroli-Mézard model: glass transition and superfluidity in a quantum lattice glass model
• Message Passing for Optimization and Control of Power Grid: Model of Distribution System with Redundancy
• Phase diagram of an Ising model with competitive interactions on a Husimi tree and its disordered counterpart
• The phase diagram of Lévy spin glasses
• Intrinsic limitations of inverse inference in the pairwise Ising spin glass
• Ensemble inequivalence in random graphs
• Out of equilibrium Phase Diagram of the Quantum Random Energy Model
• Biased landscapes for random Constraint Satisfaction Problems
• Glassy dynamics in granular compaction: sand on random graphs
• Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations
• Metastable states and T=0 hysteresis in the random-field Ising model on random graphs
• Approximate Survey Propagation for Statistical Inference
• Large Deviations of the Free-Energy in Diluted Mean-Field Spin-Glass
• AKLT Models with Quantum Spin Glass Ground States
• From one solution of a 3-satisfiability formula to a solution cluster: Frozen variables and entropy
• A Cavity Master Equation for the continuous time dynamics of discrete spins models
• Unsupervised feature learning from finite data by message passing: discontinuous versus continuous phase transition
• The large deviations of the whitening process in random constraint satisfaction problems
• Belief propagation for graph partitioning
• Structure of finite-RSB asymptotic Gibbs measures in the diluted spin glass models
• Disorder-free spin glass transitions and jamming in exactly solvable mean-field models
• Belief-Propagation and replicas for inference and learning in a kinetic Ising model with hidden spins
• Aging dynamics of heterogeneous spin models
• Coarse grained belief propagation for simulation of interacting quantum systems at all temperatures
• Dynamical replica analysis of processes on finitely connected random graphs II: Dynamics in the Griffiths phase of the diluted Ising ferromagnet
• The random field XY model on sparse random graphs shows replica symmetry breaking and marginally stable ferromagnetism
• Statistical physics of unsupervised learning with prior knowledge in neural networks
• Inference and learning in sparse systems with multiple states
• Minimal model of permutation symmetry in unsupervised learning
• Spin models on random graphs with controlled topologies beyond degree constraints
• Replica symmetry breaking in the `small world' spin glass
• The marginally stable Bethe lattice spin glass revisited
• Shortest node-disjoint paths on random graphs
• Statistical mechanics of error exponents for error-correcting codes
• Computational core and fixed-point organisation in Boolean networks
• A universal form of slow dynamics in zero-temperature random-field Ising model
• Size segregation in granular media induced by phase transition
• Analytic solution of the resolvent equations for heterogeneous random graphs: spectral and localization properties
• Reproducing size distributions of swarms of barchan dunes on Mars and Earth using a mean-field model
• Replica Cluster Variational Method: the Replica Symmetric solution for the 2D random bond Ising model
• Nonlinear $XY$ and $p$-clock models on sparse random graphs: mode-locking transition of localized waves
• Thermodynamics of the Lévy spin glass
• On the solution of a `solvable' model of an ideal glass of hard spheres displaying a jamming transition
• Bicoloring Random Hypergraphs
• The Directed Dominating Set Problem: Generalized Leaf Removal and Belief Propagation
• Replica theory for Levy spin glasses
• Dynamical replica analysis of processes on finitely connected random graphs I: vertex covering
• Metastable configurations of spin models on random graphs
• Jamming transition in granular media: A mean field approximation and numerical simulations
• Communities of solutions in single solution clusters of a random K-Satisfiability formula
• Lifshitz tails on the Bethe lattice: a combinatorial approach
• Analysis of the Relation between Quadratic Unconstrained Binary Optimization (QUBO) and the Spin Glass Ground-State Problem
• Dynamical Mean-Field Theory of Complex Systems on Sparse Directed Networks
• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• First- and second-order phase transitions in Ising models on small world networks, simulations and comparison with an effective field theory
• Characterizing and Improving Generalized Belief Propagation Algorithms on the 2D Edwards-Anderson Model
• Real Space Migdal-Kadanoff Renormalisation of Glassy Systems: Recent Results and a Critical Assessment
• How we are leading a 3-XORSAT challenge: from the energy landscape to the algorithm and its efficient implementation on GPUs
• The cavity method for large deviations
• Communication and correlation among communities
• The Phase Diagram of Random Heteropolymers
• Long range frustration in finite connectivity spin glasses: A mean field theory and its application to the random $K$-satisfiability problem
• Adaptive Thouless-Anderson-Palmer approach to inverse Ising problems with quenched random fields
• Role of fluctuations in the phase transitions of coupled plaquette spin models of glasses
• Phase Transitions in Community Detection: A Solvable Toy Model
• Structure of 1-RSB asymptotic Gibbs measures in the diluted p-spin models
• Second largest Eigenpair Statistics for Sparse Graphs
• On Cavity Approximations for Graphical Models
• Thermodynamics of spin systems on small-world hypergraphs
• The edge-disjoint path problem on random graphs by message-passing
• Cavity Method for Supersymmetry Breaking Spin Glasses
• Statistical physics of hard combinatorial optimization: The vertex cover problem
• Top Eigenpair Statistics for Weighted Sparse Graphs
• Ground-State Entropy of the Random Vertex-Cover Problem
• $T\to 0$ mean-field population dynamics approach for the random 3-satisfiability problem
• Tap Complexity, the Cavity Method and Supersymmetry
• Ergodic and localized regions in quantum spin glasses on the Bethe lattice
• Exploring Quantum Annealing Architectures: A Spin Glass Perspective
• Spectral properties of the trap model on sparse networks
• Sudden emergence of q-regular subgraphs in random graphs
• The Levy spin glass transition
• Segregation in fluidized versus tapped packs
• Aligning random graphs with a sub-tree similarity message-passing algorithm
• Glassy dynamics on networks: local spectra and return probabilities
• Spin systems on Bethe lattices
• Solving the fully-connected spherical $p$-spin model with the cavity method: equivalence with the replica results
• Aging in Spin Glasses in three, four and infinite dimensions
• Quantum Jamming: Critical Properties of a Quantum Mechanical Perceptron
• A hard-sphere model on generalized Bethe lattices: Statics
• Replica methods for loopy sparse random graphs
• Solution space structure of random constraint satisfaction problems with growing domains
• A very fast inference algorithm for finite-dimensional spin glasses: Belief Propagation on the dual lattice
• Absence of an equilibrium ferromagnetic spin glass phase in three dimensions
• Metastability of the Potts ferromagnet on random regular graphs
• Critical behavior and correlations on scale-free small-world networks. Application to network design
• Replicated Bethe Free Energy: A Variational Principle behind Survey Propagation
• A statistical physics approach to learning curves for the Inverse Ising problem
• Phase Transitions and Computational Difficulty in Random Constraint Satisfaction Problems
• Zero temperature solutions of the Edwards-Anderson model in random Husimi Lattices
• Phase transitions in the three-state Ising spin-glass model with finite connectivity
• On the number of limit cycles in diluted neural networks
• Ground State Properties of the Diluted Sherrington-Kirkpatrick Spin Glass
• Disentangling Giant Component and Finite Cluster Contributions in Sparse Matrix Spectra
• A matrix product algorithm for stochastic dynamics on networks, applied to non-equilibrium Glauber dynamics
• The statistical mechanics of random set packing and a generalization of the Karp-Sipser algorithm
• Sign problem in the Bethe approximation
• A numerical study of the overlap probability distribution and its sample-to-sample fluctuations in a mean-field model
• Antiferromagnetic Potts model on the Erdos-Renyi random graph
• Ising spin glass models versus Ising models: an effective mapping at high temperature I. General result
• Properties of atypical graphs from negative complexities
• Random-field p-spin glass model on regular random graphs
• Universality class of the mode-locked glassy random laser
• Statistical physics approach to graphical games: local and global interactions
• Diluted antiferromagnet in a ferromagnetic enviroment
• Emergence of order in random languages
• Clustering of neural codewords revealed by a first-order phase transition
• On the quantum spin glass transition on the Bethe lattice
• Thermodynamic Comparison and the Ideal Glass Transition of A Monatomic Systems Modeled as an Antiferromagnetic Ising Model on Husimi and Cubic Recursive Lattices of the Same Coordination Number
• Minimizing Unsatisfaction in Colourful Neighbourhoods
• Comparison of Gabay-Toulouse and de Almeida-Thouless instabilities for the spin glass XY model in a field on sparse random graphs
• Metastable configurations on the Bethe lattice
• Complex Replica Zeros of $\pm J$ Ising Spin Glass at Zero Temperature
• Spin Glasses on the Hypercube
• Entropy Inflection and Invisible Low-Energy States: Defensive Alliance Example
• Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
• A combined model of aggregation, fragmentation, and exchange processes: insights from analytical calculations
• Statics and dynamics of the Lebwohl-Lasher model in the Bethe approximation
• Ground-state configuration space heterogeneity of random finite-connectivity spin glasses and random constraint satisfaction problems
• Multi-body quenched disordered $XY$ and $p$-clock models on random graphs
• Glassy phases in Random Heteropolymers with correlated sequences
• Backtracking Dynamical Cavity Method
• Spectrum of the tight-binding model on Cayley Trees and comparison with Bethe Lattices
• The full replica symmetry breaking in the Ising spin glass on random regular graph
• Distribution of partition function zeros of the $\pm J$ model on the Bethe lattice
• Finite Size Effects for the Ising Model on Random Graphs with Varying Dilution
• Dynamic rewiring in small world networks
• Statistical mechanics of budget-constrained auctions
• Partition Function Expansion on Region-Graphs and Message-Passing Equations
• Recovery thresholds in the sparse planted matching problem
• Fluctuations in the random-link matching problem
• Approximating random quantum optimization problems
• Cavity approach to the Sourlas code system
• Mean-field behavior of the negative-weight percolation model on random regular graphs
• Exact calculation of the energy contributions to the T=0 random-field Ising model with metastable dynamics on the Bethe lattice
• Replica Symmetry Breaking without Replicas
• Flux distribution in metabolic networks close to optimal biomass production
• Belief-Propagation Guided Monte-Carlo Sampling
• Contagion in an interacting economy
• Statistical Mechanics of Interfering Links
• Thermal Tensor Network Simulations of the Heisenberg Model on the Bethe Lattice
• Bose-Einstein distribution, condensation transition and multiple stationary states in multiloci evolution of diploid population
• Calculation of mean spectral density for statistically uniform tree-like random models
• Near-power-law temperature dependence of the superfluid stiffness in strongly disordered superconductors
• Survey propagation at finite temperature: application to a Sourlas code as a toy model
• Finite size scaling of the de Almeida-Thouless instability in random sparse networks
• Thermodynamic Construction of an One-Step Replica-Symmetry-Breaking Solution in Finite Connectivity Spin Glasses
• Numerical Results for Spin Glass Ground States on Bethe Lattices: Gaussian Bonds
• The matrix product approximation for the dynamic cavity method
• Local overlaps, heterogeneities and the local fluctuation dissipation relations
• Mean-field phase diagram and spin glass phase of the dipolar Kagome Ising antiferromagnet
• Reversible first-order transition in Pauli percolation
• Optimal Location of Sources in Transportation Networks
• The Hubbard model on the Bethe lattice via variational uniform tree states: metal-insulator transition and a Fermi liquid
• Geometrical Frustration and Cluster Spin Glass with Random Graphs
• Next nearest neighbour Ising models on random graphs
• An improved Belief Propagation algorithm finds many Bethe states in the random field Ising model on random graphs
• Typical kernel size and number of sparse random matrices over GF(q) - a statistical physics approach
• Cavity approach to variational quantum mechanics
• Scalable Node-Disjoint and Edge-Disjoint Multi-wavelength Routing
• Spin glass phase transitions in the random feedback vertex set problem
• Optimal segmentation of directed graph and the minimum number of feedback arcs
• Generalized minimum dominating set and application in automatic text summarization
• Zero-Temperature Limit of the SUSY-breaking Complexity in Diluted Spin-Glass Models
• Circular Coloring of Random Graphs: Statistical Physics Investigation
• On The Reconstruction of Interaction Networks with Applications to Transcriptional Regulation
• Small-world hypergraphs on a bond-disordered Bethe lattice
• Spin glasses in a field show a phase transition varying the distance among real replicas (and how to exploit it to find the critical line in a field)
• Maximally flexible solutions of a random $K$-satisfiability formula
• Sparse Autoregressive Neural Networks for Classical Spin Systems
• Polymer models with competing collapse interactions on Husimi and Bethe lattices
• Improved replica bounds for the independence ratio of random regular graphs
• Griffiths-McCoy singularities, Lee-Yang zeros and the cavity method in a solvable diluted ferromagnet
• Statistical Mechanics of Semi-Supervised Clustering in Sparse Graphs
• The renormalization flow of the hierarchical Anderson model at weak disorder
• Explicit generation of the branching tree of states in spin glasses
• The planted $k$-factor problem
• RNAlike polymer model: exact calculation on the Bethe lattice
• The Fate of Articulation Points and Bredges in Percolation
• The asymptotics of the clustering transition for random constraint satisfaction problems
• Spin Glass Theory: numerical and experimental results in three-dimensional systems
• On metastable configurations of small-world networks
• Density matrix renormalization on random graphs and the quantum spin-glass transition
• Random active path model of deep neural networks with diluted binary synapses
• Dynamics of sparse Boolean networks with multi-node and self-interactions
• Biased measures for random Constraint Satisfaction Problems: larger interaction range and asymptotic expansion
• The m-component spin glass on a Bethe lattice
• Variational mean-field theory for training restricted Boltzmann machines with binary synapses
• Random-link matching problems on random regular graphs
• Belief propagation with multipoint correlations and its application to Inverse problem
• Slowly evolving random graphs II: Adaptive geometry in finite-connectivity Hopfield models
• Model fluid in a porous medium: results for a Bethe lattice
• Message-Passing on Hypergraphs: Detectability, Phase Transitions and Higher-Order Information
• Solution of Disordered Microphases in the Bethe approximation
• Low-temperature excitations within the Bethe approximation
• A hierarchical version of the de Finetti and Aldous-Hoover representations
• Long-range frustration in T=0 first-step replica-symmetry-broken solutions of finite-connectivity spin glasses
• The role of idiotypic interactions in the adaptive immune system: a belief-propagation approach
• Adversarial Satisfiability Problem
• Nonequilibrium dynamics of the Ising model on heterogeneous networks with an arbitrary distribution of threshold noise
• Boltzmann distribution of free energies in a finite-connectivity spin-glass system and the cavity approach
• Statistical Physics of Group Testing
• A spin glass approach to the directed feedback vertex set problem
• Counting and Hardness-of-Finding Fixed Points in Cellular Automata on Random Graphs
• Improved mean-field dynamical equations are able to detect the two-steps relaxation in glassy dynamics at low temperatures
• Counting solutions from finite samplings
• Equilibrium properties of disordered spin models with two scale interactions
• The Ising spin glass on random graphs at zero temperature: not all spins are glassy in the glassy phase
• Dynamics of an Ising Spin Glass on the Bethe Lattice
• A Random Walk Perspective on Hide-and-Seek Games
• Spin-glass model for the C-dismantling problem
• Palette-colouring: a belief-propagation approach
• Detectability of Macroscopic Structures in Directed Asymmetric Stochastic Block Model
• Feedback arcs and node hierarchy in directed networks
• Phase diagram and metastability of the Ising model on two coupled networks
• Theory of population coupling and applications to describe high order correlations in large populations of interacting neurons
• Statistical-mechanical Analysis of Linear Programming Relaxation for Combinatorial Optimization Problems
• A simplified Parisi Ansatz
• Statics and dynamics of selfish interactions in distributed service systems
• Data-driven effective model shows a liquid-like deep learning
• Experimental Measures of Topological Sector Fluctuations in the F-Model
• Computing loop corrections by message passing
• The network source location problem: ground state energy, entropy and effects of freezing
• Boolean decision problems with competing interactions on scale-free networks: Critical thermodynamics
• Replica theory for learning curves for Gaussian processes on random graphs
• Realizing interdependent couplings as thermal or higher-order interactions
• Equivalence between algorithmic instability and transition to replica symmetry breaking in perceptron learning systems
• Local excitations in mean field spin glasses
• Local sign stability and its implications for spectra of sparse random graphs and stability of ecosystems
• Subdiffusive spin transport in disordered classical Heisenberg chains
• Effect of Constraint Relaxation on the Minimum Vertex Cover Problem in Random Graphs
• Thermodynamics of the Fredrickson-Andersen Model on the Bethe Lattice
• SWAP algorithm for lattice spin models
• Analytical solution to Heisenberg spin glass models on sparse random graphs and their de Almeida-Thouless line
• Soft modes in vector spin glass models on sparse random graphs
• Thermodynamics of the Hubbard Model on the Bethe Lattice
• Composite CDMA - A statistical mechanics analysis
• Ising spin glass models versus Ising models: an effective mapping at high temperature III. Rigorous formulation and detailed proof for general graphs
• A residual-based message passing algorithm for constraint satisfaction problems
• A hard-sphere model on generalised Bethe lattices: Dynamics
• Code optimization, frozen glassy phase and improved decoding algorithms for low-density parity-check codes
• The effect of quantum fluctuations on the coloring of random graphs
• How could the replica method improve accuracy of performance assessment of channel coding?
• Target observation of complex networks
• Spectral density of equitable core-periphery graphs
• Solution space heterogeneity of the random K-satisfiability problem: Theory and simulations
• Multi-step relaxations in Glauber dynamics of a bond-diluted Ising model on a Bethe lattice
• Solvable Quantum Circuits in Tree+1 Dimensions
• Statistics of geometric clusters in the Ising model on a Bethe lattice: statistical mechanics approach
• Criticality and Heterogeneity in the Solution Space of Random Constraint Satisfaction Problems
• Typical case behaviour of spin systems in random graph and composite ensembles
• Hysteresis behavior of the random-field Ising model with 2-spin-flip dynamics: Exact results on a Bethe lattice
• Bethe free-energy approximations for disordered quantum systems
• On the $K$-sat model with large number of clauses
• Epidemic threshold and localization of the SIS model on directed complex networks
• Circumventing spin glass traps by microcanonical spontaneous symmetry breaking
• A List Referring Monte Carlo Method for Lattice Glass Models
• Critical exponents of the spin glass transition in a field at zero temperature
• Quantum Cluster Variational Method and Message Passing Algorithms Revisited
• Distribution of the order parameter in strongly disordered superconductors: An analytic theory
• Critical properties of disordered XY model on sparse random graphs
• Cavity approach to sphere packing in Hamming space
• Ising distribution as a latent variable model
• K-core attack, equilibrium K-core, and kinetically constrained spin system
• Evidence of Replica Symmetry Breaking under the Nishimori conditions in epidemic inference on graphs
• Spin-glass behaviour on random lattices
• Random Multi-Overlap Structures for Optimization problems
• A discrete model of water with two distinct glassy phases
• Ground state interface exponents of the diluted Sherrington-Kirkpatrick spin glass
• Cavity Approach to the Random Solid State
• Free energy of a diluted spin glass model with quadratic Hamiltonian
• Characterizing the asymmetry in hardness between synthesis and destruction of heteropolymers
• Phase transitions in atypical systems induced by a condensation transition on graphs
• Slow Spin Dynamics and Self-Sustained Clusters in Sparsely Connected Systems
• The replica symmetric solution for Potts models on d-regular graphs
• Approaching the Rate-Distortion Limit with Spatial Coupling, Belief propagation and Decimation
• Analytic approach for the number statistics of non-Hermitian random matrices
• Critical phenomena on heterogeneous small-world networks
• Effect of disorder on condensation in the lattice gas model on a random graph
• Survey propagation for the cascading Sourlas code
• Optimization and Physics: On the satisfiability of random Boolean formulae
• Branching random graph model of rough surfaces describes thermal properties of the effective molecular potential
• Statistical physics of loopy interactions: Independent-loop approximation and beyond
• Dynamically generated concatenated codes and their phase diagrams
• Fault Tolerance of Random Graphs with respect to Connectivity: Mean-field Approximation for Semi-dense Random Graphs
• Ising Spins on Randomly Multi-Branched Husimi Square Lattice: Thermodynamics and Phase Transition in Cross-dimensional Range
• A journey into localization, integrability and thermalization
• Properties of the full replica symmetry breaking free energy functional of the Ising spin glass on random regular graph
• Gauge-free cluster variational method by maximal messages and moment matching
• Replica bound for Ising spin glass models in one dimension
• Rate Distortion Theorem and the Multicritical Point of Spin Glass
• Statistical mechanics of LDPC codes on channels with memory
• Top eigenpair statistics of diluted Wishart matrices
• Witness of unsatisfiability for a random 3-satisfiability formula
• Biased thermodynamics can explain the behaviour of smart optimization algorithms that work above the dynamical threshold
• Calculation of 1RSB transition temperature of spin glass models on regular random graphs under the replica symmetric ansatz
• Exact results for the Ising model on a small-world network
• On one-step replica symmetry breaking in the Edwards-Anderson spin glass model
• Mismatching as a tool to enhance algorithmic performances of Monte Carlo methods for the planted clique model
• Statistical mechanics of optimization problems
• Random Multi-Overlap Structures and Cavity Fields in Diluted Spin Glasses
• Statistical mechanics of clonal expansion in lymphocyte networks modelled with slow and fast variables
• Error Exponents of Low-Density Parity-Check Codes on the Binary Erasure Channel
• Perturbed Message Passing for Constraint Satisfaction Problems
• Approaching the ground states of the random maximum two-satisfiability problem by a greedy single-spin flipping process
• Vaccination with partial transmission and social distancing on contact networks
• Academic Meeting Scheduling Using an Antiferromagnetic Potts Model
• Decision Theoretic Cutoff and ROC Analysis for Bayesian Optimal Group Testing
• Efficient inference in the transverse field Ising model
• Interacting Copies of Random Constraint Satisfaction Problems
• Fast convergence to an approximate solution by message-passing for complex optimizations
• On the replica symmetry phase of the independent set problem
• The full replica symmetry breaking solution in mean-field spin glass models
• Frustration of signed networks: How does it affect the thermodynamic properties of a system?
• Free energy expansion of the spin glass with finite connectivity for $\infty$ RSB
• Can endogenous fluctuations persist in high-diversity ecosystems?
• Long-range spin glass in a field at zero temperature
• Interplay between intraspecific suppression and environment in shaping biodiversity
• Overcoming the complexity barrier of the dynamic message-passing method in networks with fat-tailed degree distributions
• Optimal Localization of Diffusion Sources in Complex Networks
• Partitioning networks into clusters of synchronized nodes via the message-passing algorithm: an unbiased scalable approach
• Minority Takeover in Majority Dynamics: Searching for Rare Initializations via the History Passing Algorithm
• A cavity approach to optimization and inverse dynamical problems
• Bounds for diluted mean-fields spin glass models
• Forest expansion of two-body partition functions for sparse interaction graphs
• Cavity approach for modeling and fitting polymer stretching
• Cavity Method: Message Passing from a Physics Perspective
• Topological states and flat bands in exactly solvable decorated Cayley trees
• The replica symmetric solution for Orthogonally Constrained Heisenberg Model on Bethe lattice
• Spectra of Modular Random Graphs
• Nonequilibrium steady-state dynamics of Markov processes on graphs
• Estimating the size of the solution space of metabolic networks
• Mean-field theory of vector spin models on networks with arbitrary degree distributions
• Message Passing for Integrating and Assessing Renewable Generation in a Redundant Power Grid
• Dynamical Cavity Method for Hypergraphs and its Application to Quenches in the k-XOR-SAT Problem
• Statistical physics of principal minors: Cavity approach
• Blume-Emery-Griffiths model on Random Graphs
• Uncovering the non-equilibrium stationary properties in sparse Boolean networks