Potts spin glasses with 3, 4 and 5 states near $T=T_c$: expanding around the replica symmetric solution

TL;DR

This paper analytically expands the free energy of Potts spin glasses with 3 to 5 states near the critical temperature, revealing how the nature of phase transitions changes with the number of states.

Contribution

It introduces a fourth-order expansion of the free energy around the replica symmetric solution for Potts spin glasses with 3, 4, and 5 states, and analyzes the transition behavior near the critical temperature.

Findings

Derived the temperature dependence of 1RSB order parameters near $T_c$

Identified the crossover from continuous to jumpwise phase transitions with increasing states

Compared free energy expansions across different models

Abstract

Expansion for the free energy functionals of the Potts spin glass models with 3, 4 and 5 states up to the fourth order in $\delta q_{\alpha \beta }$ around the replica symmetric solution (RS) is investigated using a special quadrupole-like representation. The temperature dependence of the 1RSB order parameters is obtained in the vicinity of the point $T=T_c$ where the RS solution becomes unstable. The crossover from continuous to jumpwise behavior with increasing of number of states is derived analytically. The comparison is made of the free energy expansion for the Potts spin glass with that for other models.