A variational study of the random-field XY model

TL;DR

This paper uses a Gaussian variational method to analyze the random-field XY model across different dimensions, revealing how disorder affects long-range order and domain formation.

Contribution

It introduces a disorder-dependent variational approach to study the XY model, providing new insights into the Imry-Ma argument and domain size distribution.

Findings

Long-range order exists for dimensions greater than 4.

Below 4 dimensions, the system exhibits a marginally stable domain structure.

The approach calculates disorder-dependent correlation functions and domain size distribution.

Abstract

A disorder-dependent Gaussian variational approach is applied to the $d$-dimensional ferromagnetic XY model in a random field. The randomness yields a non extensive contribution to the variational free energy, implying a random mass term in correlation functions. The Imry-Ma low temperature result, concerning the existence ($d>4$) or absence ($d < 4$) of long-range order is obtained in a transparent way. The physical picture which emerges below $d=4$ is that of a marginally stable mixture of domains. We also calculate within this variational scheme, disorder dependent correlation functions, as well as the probability distribution of the Imry-Ma domain size.