Tricritical point of J1-J2 Ising model on hyperbolic lattice

TL;DR

This study investigates the phase transition behavior of the frustrated J1-J2 Ising model on hyperbolic lattices, revealing a tricritical point where the nature of the transition changes from second-order to discontinuous.

Contribution

It identifies the existence of a tricritical point in the hyperbolic lattice J1-J2 Ising model, highlighting non-mean-field transition behavior.

Findings

Second-order phase transition for  < 0.203

Discontinuous magnetization for 0.203 <  < 1/4

Presence of a tricritical point

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 \kappa = J_2 / J_1 is less than 0.203. In the region 0.203 < \kappa < 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.