Magnetic and glassy transitions in the square-lattice XY model with random phase shifts

TL;DR

This study explores magnetic and glassy phase transitions in a disordered XY model on a square lattice, revealing universal behaviors and a multicritical point on the Nishimori line through Monte Carlo simulations.

Contribution

It provides the first detailed analysis of the XY model with random phase shifts, identifying universal and disorder-dependent critical behaviors and the location of the multicritical point.

Findings

Magnetic correlations follow Kosterlitz-Thouless universality.

Overlap correlations exhibit disorder-dependent criticality.

Universal zero-temperature glassy transition at high disorder.

Abstract

We investigate the magnetic and glassy transitions of the square-lattice XY model in the presence of random phase shifts. We consider two different random-shift distributions: the Gaussian distribution and a slightly different distribution (cosine distribution) which allows the exact determination of the Nishimori line where magnetic and overlap correlation functions are equal. We perform Monte Carlo simulations for several values of the temperature and of the variance of the disorder distribution, in the paramagnetic phase close to the magnetic and glassy transition lines. We find that, along the transition line separating the paramagnetic and the quasi-long-range order phases, magnetic correlation functions show a universal Kosterlitz-Thouless behavior as in the pure XY model, while overlap correlations show a disorder-dependent critical behavior. This behavior is observed up to a multicritical point which, in the cosine model, lies on the Nishimori line. Finally, for large values of the disorder variance, we observe a universal zero-temperature glassy critical transition, which is in the same universality class as that occurring in the gauge-glass model.