Finite-size scaling critical behavior of randomly pinned spin-density waves

We have performed Monte Carlo studies of the three-dimensional XY model with random uniaxial anisotropy, which is a model for randomly pinned spin-density waves. We study LxLxL simple cubic lattices using L values in the range 16-64, and with random anisotropy strengths of D/2J=1, 2, 3, 6, and infinity. There is a well-defined finite-temperature critical point, T-c, for each of 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 infinity. 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.