Weak correlation effects in the Ising model on triangular-tiled hyperbolic lattices

Abstract

The Ising model is studied on a series of hyperbolic two-dimensional lattices which are formed by tessellation of triangles on negatively curved surfaces. In order to treat the hyperbolic lattices, we propose a generalization of the corner transfer matrix renormalization group method using a recursive construction of asymmetric transfer matrices. Studying the phase transition, the mean-field universality is captured by means of a precise analysis of thermodynamic functions. The correlation functions and the density matrix spectra always decay exponentially even at the transition point, whereas power law behavior characterizes criticality on the Euclidean flat geometry. We confirm the absence of a finite correlation length in the limit of infinite negative Gaussian curvature.

9 pages, 13 figures

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• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• Mean-field universality class induced by weak hyperbolic curvatures
• Tensor product variational formulation applied to pentagonal lattice
• Free Energy Analysis of Spin Models on Hyperbolic Lattice Geometries
• Critical Phenomena in Hyperbolic Space
• Holographic analysis of boundary correlation functions for the hyperbolic-lattice Ising model
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• Boundary-field-driven control of discontinuous phase transitions on hyperbolic lattices
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• Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet
• Phase separation on a hyperbolic lattice
• Vertex Representation of Hyperbolic Tensor Networks
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• Tensor-Network study of Ising model on infinite hyperbolic dodecahedral lattice
• Simplex Crystal Ground State and Magnetization Plateaus in the Spin-$1/2$ Heisenberg Model on the Ruby Lattice