High-temperature expansion of the magnetic susceptibility and higher moments of the correlation function for the two-dimensionalXYmodel

2008/07/29 by H. Arisue
Mathematics · Physics and Astronomy · #Physics of Superconductivity and Magnetism #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.79.011107

13 pages, 8 Postscript figures

arxiv created 2008/07/29 · openalex publication_date 2009/01/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We calculate the high-temperature series of the magnetic susceptibility and the second and fourth moments of the correlation function for the XY model on the square lattice to order beta;33 by applying the improved algorithm of the finite lattice method. The long series allow us to estimate the inverse critical temperature as beta_c=1.1200(1) , which is consistent with the most precise value given previously by the Monte Carlo simulation. The critical exponent for the multiplicative logarithmic correction is evaluated to be theta=0.054(10) , which is consistent with the renormalization group prediction of theta=1/16 .

Citations

• Low-temperature expansion of the free energy in the ASOS model
• The two-dimensionalXYmodel at the transition temperature: a high-precision Monte Carlo study
• New Cluster Expansion Method in Lattice Gauge Theory
• Low-temperature expansions for Potts models
• The critical properties of the two-dimensional xy model
• Finite-Size Scaling in Two-Dimensional Superfluids
• Computing the Roughening Transition of Ising and Solid-On-Solid Models by BCSOS Model Matching
• Ordering, metastability and phase transitions in two-dimensional systems