Phase Transition of the Ising model on a Hyperbolic Lattice

TL;DR

This paper investigates the phase transition of the Ising model on a hyperbolic lattice using CTMRG, revealing mean-field behavior with finite correlation length and entanglement entropy at the transition.

Contribution

It demonstrates the phase transition characteristics of the Ising model on a hyperbolic lattice using the CTMRG method, highlighting unique finite entanglement properties.

Findings

Correlation length remains finite at the transition

Entanglement entropy remains finite at the transition

Mean-field like behavior observed at the transition

Abstract

The matrix product structure is considered on a regular lattice in the hyperbolic plane. The phase transition of the Ising model is observed on the hyperbolic $(5, 4)$ lattice by means of the corner-transfer-matrix renormalization group (CTMRG) method. Calculated correlation length is always finite even at the transition temperature, where mean-field like behavior is observed. The entanglement entropy is also always finite.