Phase transition of the q-state clock model: duality and tensor renormalization

Abstract

We investigate the critical behavior and the duality property of the ferromagnetic $q$-state clock model on the square lattice based on the tensor-network formalism. From the entanglement spectra of local tensors defined in the original and dual lattices, we obtain the exact self-dual points for the model with $q\le 5$ and approximate self-dual points for $q\ge 6$. We calculate accurately the lower and upper critical temperatures for the six-state clock model from the fixed-point tensors determined using the higher-order tensor renormalization group method and compare with other numerical results.

5 pages, 4 figures

References in corpus (3)

• Tensor renormalization group approach to 2D classical lattice models
• Non-Kosterlitz-Thouless transitions for the $q$-state clock models
• DMRG study of the Berezinskii-Kosterlitz-Thouless transitions of the 2D five-state clock model

Cited by in corpus (4)

• Variational corner transfer matrix renormalization group method for classical statistical models
• Tensor Network Based Finite-Size Scaling for Two-Dimensional Classical Models
• ${\mathbb{Z}}_N$ lattice gauge theory in a ladder geometry
• Kosterlitz-Thouless phase and $Z_d$ topological quantum phase