Tricritical point of J1-J2 Ising model on hyperbolic lattice

Abstract

A ferromagnetic-paramagnetic phase transition of the two-dimensional frustrated Ising model on a hyperbolic lattice is investigated by use of the corner transfer matrix renormalization group method. The model contains ferromagnetic nearest-neighbor interaction J_1 and the competing antiferromagnetic interaction J_2. A mean-field like second-order phase transition is observed when the ratio κ= J_2 / J_1 is less than 0.203. In the region 0.203 < κ< 1/4, the spontaneous magnetization is discontinuous at the transition temperature. Such tricritical behavior suggests that the phase transitions on hyperbolic lattices need not always be mean-field like.

arXiv comment7 pages, 13 figures, submitted to Phys. Rev. E

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• Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices
• Thermodynamics and structure of simple liquids in the hyperbolic plane
• Mean-field universality class induced by weak hyperbolic curvatures
• Critical Phenomena in Hyperbolic Space
• Anisotropic deformation of the 6-state clock model: Tricritical-point classification
• Higher-dimensional Euclidean and non-Euclidean structures in planar circuit quantum electrodynamics
• Constraint percolation on hyperbolic lattices
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• Classical spin liquids from frustrated Ising models in hyperbolic space