Scaling Behavior in the 3D Random Field XY Model

2018/01/05 by Ronald Fisch, Fisch, Ronald
Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1801.01817

openalex publication_date 2018/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We have performed studies of the 3D random field XY model on L × L × 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. The results indicate the existence of an approximately logarithmic divergence of S ( k ) as k → 0. This suggests that the lower critical dimension for long range order in this model is three.

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