High-precision Monte Carlo study of the three-dimensional XY model on GPU

2012/11/05 by Ti-Yen Lan, Lan, Ti-Yen, Yun-Da Hsieh +3
Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum, superfluid, helium dynamics #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1211.0780

openalex publication_date 2012/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We perform large-scale Monte Carlo simulations of the classical XY model on a three-dimensional L× L × L cubic lattice using the graphics processing unit (GPU). By the combination of Metropolis single-spin flip, over-relaxation and parallel-tempering methods, we simulate systems up to L=160. Performing the finite-size scaling analysis, we obtain estimates of the critical exponents for the three-dimensional XY universality class: α=-0.01293(48) and ν=0.67098(16). Our estimate for the correlation-length exponent ν, in contrast to previous theoretical estimates, agrees with the most recent experimental estimate ν_{\rm exp}=0.6709(1) at the superfluid transition of ⁴He in a microgravity environment.

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