Tensor renormalization group study of classical XY model on the square lattice

Abstract

Using the tensor renormalization group method based on the higher-order singular value decom- position, we have studied the thermodynamic properties of the continuous XY model on the square lattice. The temperature dependence of the free energy, the internal energy and the specific heat agree with the Monte Carlo calculations. From the field dependence of the magnetic susceptibility, we find the Kosterlitz-Thouless transition temperature to be 0.8921 \pm 0.0019, consistent with the Monte Carlo as well as the high temperature series expansion results. At the transition temperature, the critical exponent δis estimated as 14.5, close to the analytic value by Kosterlitz.

5 pages, 6 figures

References in corpus (8)

• Tensor renormalization group approach to 2D classical lattice models
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Exact blocking formulas for spin and gauge models
• Large-scale Monte Carlo simulation of two-dimensional classical XY model using multiple GPUs
• Accurate exponents from approximate tensor renormalizations
• High-temperature expansion of the magnetic susceptibility and higher moments of the correlation function for the two-dimensional XY model
• High-temperature expansions through order 24 for the two-dimensional classical XY model on the square lattice
• High-Temperature Expansion of the Free Energy in the Two-Dimensional XY Model

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