Replica analysis of the generalized p-spin interaction glass model

TL;DR

This paper analyzes the stability of replica symmetry breaking solutions in generalized p-spin glass models, revealing that transition types depend on operator symmetry, interaction number, and properties.

Contribution

It introduces a detailed analysis of how operator symmetry and interaction complexity influence phase transitions in generalized p-spin models.

Findings

Transition type depends on operator reflection symmetry.

Number of interacting operators affects stability.

Transition characteristics vary with operator properties.

Abstract

We investigate stability of replica symmetry breaking solutions in generalized $p$-spin models. It is shown that the kind of the transition to the one-step replica symmetry breaking state depends not only on the presence or absence of the reflection symmetry of the generalized "spin"-operators $\hat{U}$ but on the number of interacting operators and their individual characteristics.