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Using the tensor renormalization group method based on the higher-ordersingular value decom- position, we have studied the thermodynamic properties ofthe continuous XY model on the square lattice. The temperature dependence ofthe free energy, the internal energy and the specific heat agree with the MonteCarlo 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 seriesexpansion results. At the transition temperature, the critical exponent \deltais estimated as 14.5, close to the analytic value by Kosterlitz.

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