Disorder Effects in Dynamical Restoration of Spontaneously Broken Continuous Symmetry

TL;DR

This paper investigates how quenched disorder affects the dynamical restoration of continuous symmetry in the Euclidean quantum $O(N)$ model, revealing critical behavior and scale invariance in the presence of disorder at low temperatures.

Contribution

It demonstrates, within a one-loop approximation, that certain moments of the partition function induce critical behavior and scale invariance due to disorder correlations.

Findings

Identification of moments leading to critical behavior

Disorder induces generic scale invariance in massive modes

Critical phenomena emerge in the presence of quenched disorder

Abstract

We discuss the Euclidean quantum $O(N)$ model with $N=2$ in a continuous broken symmetry phase. We study the system at low temperatures in the presence of quenched disorder linearly coupled to the scalar field. Performing an average over the ensemble of all realizations of the disorder, we represent the average free energy in terms of a series of the moments of the partition function. In the one-loop approximation, we prove that there is a denumerable collection of moments that lead the system to develop critical behavior. Our results indicate that in an equilibrium system, the strongly correlation of the disorder in imaginary produces generic scale invariance in the massive modes.