Spin glass models with ferromagnetically biased couplings on the Bethe lattice: analytic solutions and numerical simulations

Abstract

We derive the zero-temperature phase diagram of spin glass models with a generic fraction of ferromagnetic interactions on the Bethe lattice. We use the cavity method at the level of one-step replica symmetry breaking (1RSB) and we find three phases: A replica-symmetric (RS) ferromagnetic one, a magnetized spin glass one (the so-called mixed phase), and an unmagnetized spin glass one. We are able to give analytic expressions for the critical point where the RS phase becomes unstable with respect to 1RSB solutions: we also clarify the mechanism inducing such a phase transition. Finally we compare our analytical results with the outcomes of a numerical algorithm especially designed for finding ground states in an efficient way, stressing weak points in the use of such numerical tools for discovering RSB effects. Some of the analytical results are given for generic connectivity.

arXiv comment22 pages, 10 figures

References in corpus (12)

• The Bethe lattice spin glass revisited
• The structural glass transition and the entropy of the metastable states
• On the nature of the low-temperature phase in discontinuous mean-field spin glasses
• Rigorous decimation-based construction of ground pure states for spin glass models on random lattices
• Instability of one-step replica-symmetry-broken phase in satisfiability problems
• Exact solutions for diluted spin glasses and optimization problems
• Hiding solutions in random satisfiability problems: A statistical mechanics approach
• Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model
• Renormalization for Discrete Optimization
• Numerical Results for Ground States of Spin Glasses on Bethe Lattices
• Ground state of the Bethe-lattice spin glass and running time of an exact optimization algorithm
• Absence of an equilibrium ferromagnetic spin glass phase in three dimensions

Cited by in corpus (26)

• Critical phenomena in complex networks
• Statistical physics of inference: Thresholds and algorithms
• Phase Transitions in the Coloring of Random Graphs
• Network Controllability Is Determined by the Density of Low In-Degree and Out-Degree Nodes
• The number of matchings in random graphs
• Clusters of solutions and replica symmetry breaking in random k-satisfiability
• The critical behavior of three-dimensional Ising spin glass models
• Generalization of the cavity method for adiabatic evolution of Gibbs states
• The 3D +-J Ising model at the ferromagnetic transition line
• On the number of circuits in random graphs
• Numerical studies of a one-dimensional 3-spin spin-glass model with long-range interactions
• Finite-Connectivity Spin-Glass Phase Diagrams and Low Density Parity Check Codes
• Magnetic-glassy multicritical behavior of the three-dimensional +- J Ising model
• Conjecture on the maximum cut and bisection width in random regular graphs
• Approximating the XY model on a random graph with a $q$-state clock model
• The random field XY model on sparse random graphs shows replica symmetry breaking and marginally stable ferromagnetism
• A very fast inference algorithm for finite-dimensional spin glasses: Belief Propagation on the dual lattice
• Zero temperature solutions of the Edwards-Anderson model in random Husimi Lattices
• Random-field p-spin glass model on regular random graphs
• Distribution of partition function zeros of the $\pm J$ model on the Bethe lattice
• Survey propagation at finite temperature: application to a Sourlas code as a toy model
• Clusterization, frustration and collectivity in random networks
• Entropic long range order in a 3D spin glass model
• Survey propagation for the cascading Sourlas code
• Spin-glass behaviour on random lattices
• Statistical mechanics of the minimum vertex cover problem in stochastic block models