The phase diagram of L\'evy spin glasses

TL;DR

This paper analyzes the phase diagram of Le9vy spin glasses using the replica and cavity methods, revealing a hybrid interaction structure with strong and weak bonds, and provides a complete phase diagram including symmetry breaking.

Contribution

It introduces a novel solution method for Le9vy spin glasses that captures the hybrid bond behavior and determines the full replica symmetric and symmetry breaking phase diagrams.

Findings

Complete replica symmetric phase diagram obtained

Identification of the symmetry breaking line

Comparison with simulations confirms the theoretical results

Abstract

We study the L\'evy spin-glass model with the replica and the cavity method. In this model each spin interacts through a finite number of strong bonds and an infinite number of weak bonds. This hybrid behaviour of L\'evy spin glasses becomes transparent in our solution: the local field contains a part propagating along a backbone of strong bonds and a Gaussian noise term due to weak bonds. Our method allows to determine the complete replica symmetric phase diagram, the replica symmetry breaking line and the entropy. The results are compared with simulations and previous calculations using a Gaussian ansatz for the distribution of fields.