Glassy Freezing and Long-Range Order in the 3D Random Field $XY$ Model

TL;DR

This study uses Monte Carlo simulations to investigate the 3D random field XY model, revealing glassy freezing above a critical temperature and long-range order below, relevant for understanding disordered condensed matter systems.

Contribution

It provides new Monte Carlo evidence of phase behavior in the 3D random field XY model across different disorder strengths, connecting to physical systems like superconductors and quasicrystals.

Findings

Glassy freezing observed above T_c

Long-range order established below T_c

Consistent results across different disorder distributions

Abstract

Monte Carlo studies of the 3D random field $XY$ model on simple cubic lattices of size $64^3$, using two different isotropic random-field probability distributions of moderate strength, show a glassy freezing behavior above $T_c$, and long-range order below $T_c$, consistent with our earlier results for weaker and stronger random fields. This model should describe random pinning in vortex lattices in type-II superconducting alloys, charge-density wave materials, and decagonal quasicrystals.