Finite-Size Scaling Critical Behavior of Randomly Pinned Spin-Density Waves

TL;DR

This study uses Monte Carlo simulations to analyze the critical behavior of the 3D XY model with random anisotropy, revealing finite-temperature phase transitions and ferromagnetic ordering tendencies.

Contribution

It provides the first finite-size scaling analysis of the critical behavior in a 3D XY model with random uniaxial anisotropy, including detailed scaling functions and phase transition characteristics.

Findings

Finite-temperature critical points identified for various anisotropy strengths.

Scaling functions show good collapse for strong anisotropy cases.

Evidence of ferromagnetic order below critical temperature for large systems.

Abstract

We have performed Monte Carlo studies of the 3D $XY$ model with random uniaxial anisotropy, which is a model for randomly pinned spin-density waves. We study $L \times L \times L$ simple cubic lattices, using $L$ values in the range 16 to 64, and with random anisotropy strengths of $D / 2 J$ = 1, 2, 3, 6 and $\infty$. There is a well-defined finite temperature critical point, $T_c$, for each these values of $D / 2 J$. We present results for the angle-averaged magnetic structure factor, $S (k)$ at $T_c$ for $L = 64$. We also use finite-size scaling analysis to study scaling functions for the critical behavior of the specific heat, the magnetization and the longitudinal magnetic susceptibility. Good data collapse of the scaling functions over a wide range of $T$ is seen for $D / 2 J$ = 6 and $\infty$. For our finite values of $D / 2 J$ the scaled magnetization function increases with $L$ below $T_c$, and appears to approach an $L$-independent limit for large $L$. This suggests that the system is ferromagnetic below $T_c$.