Scaling beyond the Imry-Ma length: Evidence of a glassy first-order phase transition in the $3D$ Random Field $XY$ Model

Ronald Fisch

Published 2018-01-05Version 1

We have performed studies of the 3D random field $XY$ model on $L \times L \times L$ simple cubic lattices with periodic boundary conditions, with a random field strength of $h_r$ = 1.875, for $L = 64$ and $L = 96$, using a parallelized Monte Carlo algorithm. We present results for the angle-averaged magnetic structure factor, $S ( k )$ at $T = 1.00$, which appears to be the temperature at which small jumps in the magnetization per spin and the energy per spin occur. It is likely that the sizes of these jumps will scale to zero as $L$ continues to grow, as predicted by Aizenman and Wehr. However, the data are not yet accurate enough to allow an estimate of the rate at which this occurs.