Phase Transition of the Ising model on a Hyperbolic Lattice

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.

4 pages, 3 figures

References in corpus (6)

• Periodic boundary conditions on the pseudosphere
• Ising model on hyperbolic lattice studied by corner transfer matrix renormalization group method
• Monte-Carlo simulation study of the two-stage percolation transition in enhanced binary trees
• Hyperbolic Deformation on Quantum Lattice Hamiltonians
• Tricritical point of J1-J2 Ising model on hyperbolic lattice
• Novel scaling behavior of the Ising model on curved surfaces

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• Weak correlation effects in the Ising model on triangular-tiled hyperbolic lattices
• Variational optimization of tensor-network states with the honeycomb-lattice corner transfer matrix
• Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices
• Superstable cycles for antiferromagnetic Q-state Potts and three-site interaction Ising models on recursive lattices
• Mean-field universality class induced by weak hyperbolic curvatures
• Tensor product variational formulation applied to pentagonal lattice
• Holographic analysis of boundary correlation functions for the hyperbolic-lattice Ising model
• Statistical Mechanics Approach to the Holographic Renormalization Group: Bethe Lattice Ising Model and p-adic AdS/CFT
• Emergence of a Boundary-Sensitive Phase in Hyperbolic Ising Models
• Vertex Representation of Hyperbolic Tensor Networks
• Tensor-Network study of Ising model on infinite hyperbolic dodecahedral lattice