2010/01/21 by Vincenzo Alba, Andrea Pelissetto, Ettore Vicari · 19 citations
Materials Science · Physics and Astronomy · #Gaussian #Material Dynamics and Properties #Monte Carlo method #Multicritical point #Paramagnetism #Phase (matter) #Phase transition #Physics of Superconductivity and Magnetism #Spin glass #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2010/03/p03006
published in Journal of Statistical Mechanics Theory and Experiment 2010(03), P03006 (Institute of Physics) · 45 pages
arxiv created 2010/01/21 · openalex publication_date 2010/03/11 · arxiv updated 2015/05/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/08
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.