High-temperature expansion of the magnetic susceptibility and higher moments of the correlation function for the two-dimensional XY model

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 $\theta =1/16$.

arXiv comment13 pages, 8 Postscript figures

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• Controlling sign problems in spin models using tensor renormalization
• Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks
• Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitions
• Resolving the Berezinskii-Kosterlitz-Thouless transition in the 2D XY model with tensor-network based level spectroscopy
• Critical analysis of two-dimensional classical XY model
• Clock model interpolation and symmetry breaking in O(2) models
• Scaling Theories of Kosterlitz-Thouless Phase Transitions
• Hybrid Berezinskii-Kosterlitz-Thouless and Ising topological phase transition in the generalized two-dimensional XY model using tensor networks
• Berezinskii-Kosterlitz-Thouless-like percolation transitions in the two-dimensional XY model
• Tensor network calculation of the logarithmic correction exponent in the XY model
• Percolation of the two-dimensional XY model in the flow representation
• Extended scaling behavior of the spatially-anisotropic classical XY model in the crossover from three to two dimensions