Phase transitions in XY models with randomly oriented crystal fields

TL;DR

This paper analyzes phase transitions in XY models with random crystal fields, revealing insensitivity of critical temperature to disorder distribution and identifying a rich phase diagram with four distinct phases.

Contribution

It provides a new representation of free energy for XY models with arbitrary disorder distributions and explores the effects of disorder strength and asymmetry on phase behavior.

Findings

Critical temperature is insensitive to disorder distribution for many cases.

Specific heat behavior depends on the finiteness of D at zero temperature.

Identified four phases including a novel canted mixed phase with disorder dependence.

Abstract

We obtain a representation of the free energy of an XY model on a fully connected graph with spins subjected to a random crystal field of strength $D$ and with random orientation $\alpha$. Results are obtained for an arbitrary probability distribution of the disorder using large deviation theory, for any $D$. We show that the critical temperature is insensitive to the nature and strength of the distribution $p(\alpha)$, for a large family of distributions which includes quadriperiodic distributions, with $p(\alpha)=p(\alpha+\frac{\pi}{2})$, which includes the uniform and symmetric bimodal distributions. The specific heat vanishes as temperature $T \rightarrow 0$ if $D$ is infinite, but approaches a constant if $D$ is finite. We also studied the effect of asymmetry on a bimodal distribution of the orientation of the random crystal field and obtained the phase diagram comprising four phases: a mixed phase (in which spins are canted at angles which depend on the degree of disorder), an $x$-Ising phase, a $y$-Ising phase and a paramagnetic phase, all of which meet at a tetra-critical point. The canted mixed phase is present for all finite $D$, but vanishes when $D \rightarrow \infty$.