Structure Factor of the 3D Random Field XY Model

TL;DR

This study uses Monte Carlo simulations to investigate the phase transition and magnetic structure factor in the 3D random field XY model, revealing a possible ferromagnetic transition influenced by Griffiths singularities.

Contribution

First Monte Carlo analysis of the 3D random field XY model showing evidence of a phase transition with unique characteristics.

Findings

Indication of a phase transition into a ferromagnetic state.

Discontinuous jump of magnetization squared at transition.

Presence of Griffiths singularity facilitating the transition.

Abstract

We have performed Monte Carlo studies of the 3D random field XY model on $L \times L \times L$ simple cubic lattices, with random field strengths of $h_r$ = 1 and 2. We present results for the angle-averaged magnetic structure factor, $S (k)$ at $L = 64$. Our results appear to indicate a phase transition into a ferromagnetic state. This is made possible by the existence of a Griffiths singularity. It appears that at the phase transition $M^2$ jumps to zero discontinuously, with a latent heat which is probably subextensive.