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

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 $D/2J$ = 1, 2, 3, 6 and $\infty$. There is a well-defined finite temperature critical point, $T_c$, for each these values of $D/2J$. 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 $D/2J$ = 6 and $\infty$. For our finite values of $D/2J$ 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 $T_c$.

21 pages in single column format, 20 .eps files, revised and expanded, errors corrected, submitted to PRB

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