Replica Field Theory for Deterministic Models: Binary Sequences with Low Autocorrelation

Abstract

We study systems without quenched disorder with a complex landscape, and we use replica symmetry theory to describe them. We discuss the Golay-Bernasconi-Derrida approximation of the low autocorrelation model, and we reconstruct it by using replica calculations. Then we consider the full model, its low $T$ properties (with the help of number theory) and a Hartree-Fock resummation of the high-temperature series. We show that replica theory allows to solve the model in the high $T$ phase. Our solution is based on one-link integral techniques, and is based on substituting a Fourier transform with a generic unitary transformation. We discuss this approach as a powerful tool to describe systems with a complex landscape in the absence of quenched disorder.

42 pages, uufile with eps figures added in figures, ROM2F/94/15

References in corpus (3)

• Replica Field Theory for Deterministic Models (II): A Non-Random Spin Glass with Glassy Behavior
• On the 3d Ising Spin Glass
• Dynamical Behaviour of Low Autocorrelation Models

Cited by in corpus (88)

• Models of traps and glass phenomenology
• Langevin Equation for the Density of a System of Interacting Langevin Processes
• The structural glass transition and the entropy of the metastable states
• Thermodynamics of glasses: a first principle computation
• Mode-Coupling Approximations, Glass Theory and Disordered Systems
• Replica Field Theory for Deterministic Models (II): A Non-Random Spin Glass with Glassy Behavior
• A first principle computation of the thermodynamics of glasses
• Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences
• Glassiness in a model without energy barriers
• A ferromagnet with a glass transition
• A tentative Replica Study of the Glass Transition
• Mean-Field Equations for Spin Models with Orthogonal Interaction Matrices
• Statistical Physics of Structural Glasses
• Constrained Boltzmann-Gibbs measures and effective potential for glasses in hypernetted chain approximation and numerical simulations
• Effective potential in glassy systems: theory and simulations
• Mode-coupling theory for the slow collective dynamics of fluids adsorbed in disordered porous media
• Exhaustive search for low autocorrelation binary sequences
• Spatially heterogeneous ages in glassy dynamics
• General phase-diagram of multimodal ordered and disordered lasers in closed and open cavities
• Complexity of waves in nonlinear disordered media
• Toy model for the mean-field theory of hard-sphere liquids
• Phase Transition in the ABC Model
• On the critical slowing down exponents of mode coupling theory
• Inherent structures and non-equilibrium dynamics of 1D constrained kinetic models: a comparison study
• Low Autocorrelation Binary Sequences
• Quantum phase transition in spin glasses with multi-spin interactions
• Kob-Andersen model: a non-standard mechanism for the glassy transition
• High-temperature Expansions and Message Passing Algorithms
• Cryptographical Properties of Ising Spin Systems
• Fragile-glass behavior of a short range $p$-spin model
• DYNAMICAL SOLUTION OF A MODEL WITHOUT ENERGY BARRIERS
• Statistical mechanics models for multimode lasers and random lasers
• $D$-dimensional Arrays of Josephson Junctions, Spin Glasses and $q$-deformed Harmonic Oscillators
• Universality and its Origins at the Amorphous Solidification Transition
• The jamming transition in high dimension: an analytical study of the TAP equations and the effective thermodynamic potential
• Classical Glasses, Black Holes, and Strange Quantum Liquids
• Low-Autocorrelation Binary Sequences: On Improved Merit Factors and Runtime Predictions to Achieve Them
• Landscape statistics of the low autocorrelated binary string problem
• Finitely coordinated models for low-temperature phases of amorphous systems
• Evidence of a Critical time in Constrained Kinetic Ising models
• On the Approach to the Equilibrium and the Equilibrium Properties of a Glass-Forming Model
• Inverse Freezing in Mean-Field Models of Fragile Glasses
• The Fully Frustrated Hypercubic Model is Glassy and Aging at Large $D$
• Statistical physics of nonlinear wave interaction
• On the ground states of the Bernasconi model
• A mean-field hard-spheres model of glass
• Long time limit of equilibrium glassy dynamics and replica calculation
• Simulating Lattice Spin Models on Graphics Processing Units
• Classical many-particle systems with unique disordered ground states
• Anomalous coarsening and glassy dynamics
• Disorder-free spin glass transitions and jamming in exactly solvable mean-field models
• Glassiness and Lack of Equipartition in Random Lasers: the common roots of Ergodicity Breaking in Disordered and Non-linear Systems
• Closure of the Monte Carlo dynamical equations in the spherical Sherrington-Kirkpatrick model
• Inverse design of disordered stealthy hyperuniform spin chains
• Dynamical transition for a particle in a squared Gaussian potential
• A Non-Disordered Glassy Model with a Tunable Interaction Range
• Replica Theory and Large D Josephson Junction Hypercubic Models
• Low autocorrelated multi-phase sequences
• Self- generated disorder and structural glass formation in homopolymer globules
• Metastable States in High Order Short-Range Spin Glasses
• RKKY Interaction and Intrinsic Frustration in Non-Fermi Liquid Metals
• Glassy Random Matrix Models
• Dynamical Behaviour of Low Autocorrelation Models
• Statistics of energy levels and zero temperature dynamics for deterministic spin models with glassy behaviour
• Nonequilibrium fluctuations in small systems: From physics to biology
• Thermalization without chaos in harmonic systems
• The number of metastable states in the generalized random orthogonal model
• Self-induced glassy phase in multimodal cavity quantum electrodynamics
• Mean-field phase diagram and spin glass phase of the dipolar Kagome Ising antiferromagnet
• Energy-Decreasing Dynamics in Mean-Field Spin Models
• High Temperature Asymptotics of Orthogonal Mean-Field Spin Glasses
• On Lattice Gas Models For Disordered Systems
• Deterministic spin models with a glassy phase transition
• Damage spreading transition in glasses: a probe for the ruggedness of the configurational landscape
• Langevin dynamics of the Lebowitz-Percus model
• Ground states for a class of deterministic spin models with glassy behaviour
• Mean-field glass transition in a model liquid
• Dipole diffusion in a random electrical potential
• Random, thermodynamic and inverse first order transitions in the Blume-Capel spin-glass
• Crossover behaviour of a one dimensional Random Energy Model
• A large-N approximated field theory for multipartite entanglement
• Quantum Annealing with chaotic driver Hamiltonians
• Lattice Gas Analogue Of SK Model: A paradigm for the glass transition
• Classical and Quantum Behavior in Mean-Field Glassy Systems
• Slow dynamics of glassy systems
• On the Static and Dynamical Transition in the Mean-Field Potts Glass
• A Solvable Model of a Glass
• Low Auto-correlation Binary Sequences explored using Warning Propagation