Replica analysis of Franz-Parisi potential for sparse systems

Abstract

We propose a method for calculating the Franz-Parisi potential for spin glass models on sparse random graphs using the replica method under the replica symmetric ansatz. The resulting self-consistent equations have the solution with the characteristic structure of multi-body overlaps, and the self-consistent equations under this solution are equivalent to the one-step replica symmetry breaking (1RSB) cavity equation with Parisi parameter $x=1$. This method is useful for the evaluation of transition temperatures of the $p$-spin model on regular random graphs under a uniform magnetic field.

arXiv comment21 pages, 3 figures

References in corpus (14)

• Recipes for metastable states in Spin Glasses
• Phase diagram of glassy systems in an external field
• Reconstruction on trees and spin glass transition
• Clusters of solutions and replica symmetry breaking in random k-satisfiability
• A ferromagnet with a glass transition
• Exact solutions for diluted spin glasses and optimization problems
• Effective potential in glassy systems: theory and simulations
• On the cooling-schedule dependence of the dynamics of mean-field glasses
• Temperature evolution and bifurcations of metastable states in mean-field spin glasses, with connections with structural glasses
• Generalization of the cavity method for adiabatic evolution of Gibbs states
• Near optimal configurations in mean field disordered systems
• Belief propagation for graph partitioning
• Thermodynamic Construction of an One-Step Replica-Symmetry-Breaking Solution in Finite Connectivity Spin Glasses
• Calculation of 1RSB transition temperature of spin glass models on regular random graphs under the replica symmetric ansatz