Symmetry Nonrestoration in a Gross-Neveu Model with Random Chemical Potential

TL;DR

This paper investigates the symmetry behavior of the Gross-Neveu model with random chemical potential, revealing that certain symmetries are not restored at high temperature and identifying quantum phase transitions influenced by disorder strength.

Contribution

It provides new insights into symmetry nonrestoration phenomena in disordered fermionic models across different dimensions and temperature regimes.

Findings

Charge conjugation symmetry is not restored at high temperature in three dimensions.

In two dimensions, strong disorder causes a quantum phase transition affecting symmetry.

High-temperature behavior mirrors zero-temperature symmetry states for any disorder level.

Abstract

We study the symmetry behavior of the Gross-Neveu model in three and two dimensions with random chemical potential. This is equivalent to a four-fermion model with charge conjugation symmetry as well as Z_2 chiral symmetry. At high temperature the Z_2 chiral symmetry is always restored. In three dimensions the initially broken charge conjugation symmetry is not restored at high temperature, irrespective of the value of the disorder strength. In two dimensions and at zero temperature the charge conjugation symmetry undergoes a quantum phase transition from a symmetric state (for weak disorder) to a broken state (for strong disorder) as the disorder strength is varied. For any given value of disorder strength, the high-temperature behavior of the charge conjugation symmetry is the same as its zero-temperature behavior. Therefore, in two dimensions and for strong disorder strength the charge conjugation symmetry is not restored at high temperature.