The marginally stable Bethe lattice spin glass revisited

Abstract

Bethe lattice spins glasses are supposed to be marginally stable, i.e. their equilibrium probability distribution changes discontinuously when we add an external perturbation. So far the problem of a spin glass on a Bethe lattice has been studied only using an approximation where marginally stability is not present, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a marginally stable 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 approach to the Bethe lattice spin glass problem using approximations that should be hopeful consistent with marginal stability.

23 pages Revised version, hopefully clearer that the first one: six pages longer

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• Martingales for physicists: A treatise on stochastic thermodynamics and beyond
• Phase transitions in the $q$-coloring of random hypergraphs
• Dynamical Mean-Field Theory and Aging Dynamics
• Comparison of Gabay-Toulouse and de Almeida-Thouless instabilities for the spin glass XY model in a field on sparse random graphs
• Emergence of order in random languages
• (Dis)assortative Partitions on Random Regular Graphs
• The full replica symmetry breaking in the Ising spin glass on random regular graph
• The Ising spin glass on random graphs at zero temperature: not all spins are glassy in the glassy phase
• 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
• Critical properties of disordered XY model on sparse random graphs
• The full replica symmetry breaking solution in mean-field spin glass models
• Free energy expansion of the spin glass with finite connectivity for $\infty$ RSB