2010/10/15 by Hao Hu, Youjin Deng, Henk W. J. Blöte
Mathematics · Physics and Astronomy · #Classical XY model #Combinatorics #Condensed matter physics #Critical exponent #Electrical resistivity and conductivity #Exponent #Geometry #Markov Chains and Monte Carlo Methods #Mathematics #Monte Carlo method #Percolation (cognitive psychology) #Percolation critical exponents #Percolation threshold #Phase transition #Physics #Quantum mechanics #Scaling #Spin (aerodynamics) #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.83.011124
published as PhysRevE.83.011124 (2011) · 23 pages, 14 figures
arxiv created 2010/10/15 · openalex publication_date 2011/01/25 · arxiv updated 2011/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study a percolation problem on a substrate formed by two-dimensional XY spin configurations using Monte Carlo methods. For a given spin configuration, we construct percolation clusters by randomly choosing a direction x in the spin vector space, and then placing a percolation bond between nearest-neighbor sites i and j with probability p(ij)=max(0,1-e(-2Ks(i)(x)s(j)(x))), where K>0 governs the percolation process. A line of percolation thresholds K(c)(J) is found in the low-temperature range J≥J(c), where J>0 is the XY coupling strength. Analysis of the correlation function g(p)(r), defined as the probability that two sites separated by a distance r belong to the same percolation cluster, yields algebraic decay for K≥K(c)(J), and the associated critical exponent depends on J and K. Along the threshold line K(c)(J), the scaling dimension for g(p) is, within numerical uncertainties, equal to 1/8. On this basis, we conjecture that the percolation transition along the K(c)(J) line is of the Berezinskii-Kosterlitz-Thouless type.