The spherical 2+p spin glass model: an analytically solvable model with a glass-to-glass transition

Abstract

We present the detailed analysis of the spherical s+p spin glass model with two competing interactions: among p spins and among s spins. The most interesting case is the 2+p model with p > 3 for which a very rich phase diagram occurs, including, next to the paramagnetic and the glassy phase represented by the one step replica symmetry breaking ansatz typical of the spherical p-spin model, other two amorphous phases. Transitions between two contiguous phases can also be of different kind. The model can thus serve as mean-field representation of amorphous-amorphous transitions (or transitions between undercooled liquids of different structure). The model is analytically solvable everywhere in the phase space, even in the limit where the infinite replica symmetry breaking ansatz is required to yield a thermodynamically stable phase.

21 pages, 18 figures

References in corpus (23)

• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Elastic theory of flux lattices in presence of weak disorder
• Elastic Theory of pinned flux lattices
• The structural glass transition and the entropy of the metastable states
• Higher order glass-transition singularities in colloidal systems with attractive interactions
• Reentrant glass transition in a colloid-polymer mixture with depletion attractions
• The Thermodynamic Limit in Mean Field Spin Glass Models
• Measuring equilibrium properties in aging systems
• The response of glassy systems to random perturbations: A bridge between equilibrium and off-equilibrium
• Mechanical Properties of a Model of Attractive Colloidal Solutions
• Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model
• Large time off-equilibrium dynamics of a manifold in a random potential
• The spherical $2+p$ spin glass model: an exactly solvable model for glass to spin-glass transition
• Exactly solvable model of a quantum spin glass
• Replica Fourier Transforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices
• The Complexity of the Spherical $p$-spin spin glass model, revisited
• The 3-SAT problem with large number of clauses in $\infty$-replica symmetry breaking scheme
• Quenched Computation of the Complexity of the Sherrington-Kirkpatrick Model
• Modified TAP equations for the SK spin glass
• Coexistence of supersymmetric and supersymmetry-breaking states in spherical spin-glasses
• Glass glass transition and new dynamical singularity points in an analytically solvable p-spin glass like model
• Different Scenarios for Critical Glassy Dynamics
• Glassy trapping of manifolds in nonpotential random flows

Cited by in corpus (48)

• General phase-diagram of multimodal ordered and disordered lasers in closed and open cavities
• Amorphous-amorphous transition and the two-step replica symmetry breaking phase
• Classical Particle in a Box with Random Potential: exploiting rotational symmetry of replicated Hamiltonian
• The Complex Spherical 2+4 Spin Glass: a Model for Nonlinear Optics in Random Media
• Marvels and Pitfalls of the Langevin Algorithm in Noisy High-dimensional Inference
• Gradient descent dynamics in the mixed $p$-spin spherical model: finite size simulation and comparison with mean-field integration
• A thermodynamic description of colloidal glasses
• Inverse Freezing in Mean-Field Models of Fragile Glasses
• On weak ergodicity breaking in mean-field spin glasses
• How to count in hierarchical landscapes: a 'full' solution to mean-field complexity
• Replica Fourier Transform: Properties and Applications
• Interface free energies in p-spin glass models
• Distribution of rare saddles in the $p$-spin energy landscape
• Pressure induced orientational glass phase in molecular para-hydrogen
• Statistical mechanical approach to secondary processes and structural relaxation in glasses and glass formers
• On Equilibrium Dynamics of Spin-Glass Systems
• Equilibrium Fluctuations in Mean-field Disordered Models
• Comment on ``Spherical 2 + p spin-glass model: An analytically solvable model with a glass-to-glass transition''
• Exactly solvable spin-glass models with ferromagnetic couplings: the spherical multi-$p$-spin model in a self-induced field
• Arrangement of nearby minima and saddles in the mixed spherical energy landscapes
• Full versus first stage replica symmetry breaking in spin glasses
• Following states in temperature in the spherical s+p-spin glass model
• Reply to Comment on ``Spherical 2+p spin-glass model: an analytically solvable model with a glass-to-glass transition''
• Replica analysis of the generalized p-spin interaction glass model
• Critical Off-Equilibrium Dynamics in Glassy Systems
• Stability of the Parisi Solution for the Sherrington-Kirkpatrick model near T=0
• The full replica symmetry breaking in the Ising spin glass on random regular graph
• A simple spin model for three steps relaxation and secondary proccesses in glass formers
• Avalanches and hysteresis in frustrated superconductors and XY-spin-glasses
• The Super-Potts glass: a new disordered model for glass-forming liquids
• Continuous and discontinuous transitions in generalized p-spin glass models
• When is the average number of saddle points typical?
• Numerical renormalization of glassy dynamics
• Generalized Sherrington--Kirkpatrick-glass without reflection symmetry
• A constrained TAP approach for disordered spin models: application to the mixed spherical case
• Replica-symmetry breaking transitions in the large deviations of the ground-state of a spherical spin-glass
• Compressed sensing with l0-norm: statistical physics analysis and algorithms for signal recovery
• On the topology of solutions to random continuous constraint satisfaction problems
• Packing hard spheres with short-range attraction in infinite dimension: Phase structure and algorithmic implications
• Static and dynamic glass-glass transitions: a mean-field study
• Low temperature spin glass fluctuations: expanding around a spherical approximation
• Analytical Study of Momentum-Based Acceleration Methods in Paradigmatic High-Dimensional Non-Convex Problems
• Quantum criticality in photorefractive optics: vortices in laser beams and antiferromagnets
• The decoupling of the glass transitions in the two-component $p$-spin spherical model
• Nature vs. Nurture: Dynamical Evolution in Disordered Ising Ferromagnets
• Time-translation invariance symmetry breaking hidden by finite-scale singularities
• The phase diagram of compressed sensing with ${\ell }_0$-norm regularization
• Logarithmic critical slowing down in complex systems: from statics to dynamics