Quasi-long-range order in the 2D XY model with random phase shifts

TL;DR

This paper investigates the low-temperature phase of the 2D XY model with random phase shifts, demonstrating that the universal long-distance behavior is well described by the random spin-wave theory through Monte Carlo simulations.

Contribution

It provides the first comprehensive numerical validation of the random spin-wave theory for the disordered 2D XY model's low-temperature phase.

Findings

Universal quantities match analytic predictions

Good agreement with random spin-wave theory

Low-temperature phase exhibits quasi-long-range order

Abstract

We study the square-lattice XY model in the presence of random phase shifts. We consider two different disorder distributions with zero average shift and investigate the low-temperature quasi-long-range order phase which occurs for sufficiently low disorder. By means of Monte Carlo simulations we determine several universal quantities which are then compared with the analytic predictions of the random spin-wave theory. We observe a very good agreement which indicates that the universal long-distance behavior in the whole low-disorder low-temperature phase is fully described by the random spin-wave theory.