Structure factor of the three-dimensional random-fieldXYmodel: Monte Carlo calculations

Abstract

We have performed Monte Carlo studies of the three-dimensional random-field $XY$ model on $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$ 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.