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.

21 pages, 3 figures

References in corpus (3)

• Clusters of solutions and replica symmetry breaking in random k-satisfiability
• Generalization of the cavity method for adiabatic evolution of Gibbs states
• Near optimal configurations in mean field disordered systems