Critical analysis of two-dimensional classical XY model

Abstract

We consider the two-dimensional classical XY model on a square lattice in the thermodynamic limit using tensor renormalization group and precisely determine the critical temperature corresponding to the Berezinskii-Kosterlitz-Thouless (BKT) phase transition to be 0.89290(5) which is an improvement compared to earlier studies using tensor network methods.

arXiv commentv2: Minor changes with no change in final result. Accepted for publication in Journal of Statistical Mechanics. v1: 14 pages, 5 figures, and a table

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• Truncation effects in the charge representation of the O(2) model
• Clock model interpolation and symmetry breaking in O(2) models
• Collective Monte Carlo updates through tensor network renormalization
• Phase diagram of generalized XY model using tensor renormalization group
• Percolation of the two-dimensional XY model in the flow representation
• Tensor Network Renormalization Study on the Crossover in Classical Heisenberg and $\mathrm{R}{\mathrm{P}}^2$ Models in Two Dimensions
• Helicity modulus and chiral symmetry breaking for boundary conditions with finite twist
• Probing phase transitions with correlations in configuration space
• Initial tensor construction and dependence of the tensor renormalization group on initial tensors
• Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions
• Berezinskii-Kosterlitz-Thouless Renormalization Group Flow at a Quantum Phase Transition