One-step replica symmetry breaking solution of the quadrupolar glass model

TL;DR

This paper develops a one-step replica symmetry breaking solution for the quadrupolar glass model, analyzing phase transitions and stability, revealing complex behavior with multiple transitions depending on the quadrupole dimension.

Contribution

It introduces a simple one-step replica symmetry breaking ansatz to study phase transitions in the quadrupolar glass model, highlighting new insights into transition types and stability.

Findings

Identification of continuous and discontinuous transitions below and above a critical quadrupole dimension m*

Discovery of two transitions for m>m*, including a thermodynamic discontinuous transition without latent heat

Determination of a higher temperature dynamical or glass transition with a discontinuous order parameter jump

Abstract

We consider the quadrupolar glass model with infinite-range random interaction. Introducing a simple one-step replica symmetry breaking ansatz we investigate the para-glass continuous (discontinuous) transition which occurs below (above) a critical value of the quadrupole dimension m*. By using a mean-field approximation we study the stability of the one-step replica symmetry breaking solution and show that for m>m* there are two transitions. The thermodynamic transition is discontinuous but there is no latent heat. At a higher temperature we find the dynamical or glass transition temperature and the corresponding discontinuous jump of the order parameter.