Spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction and quartic Ising interactions as the exactly soluble zero-field eight-vertex model

TL;DR

This paper exactly solves a spin-1/2 Ising-Heisenberg model with pair XYZ and quartic interactions by mapping it to the eight-vertex model, revealing complex critical behaviors including re-entrant transitions and quantum critical points.

Contribution

It introduces an exact solution for a complex quantum spin model with novel critical phenomena, expanding understanding of phase transitions in such systems.

Findings

Re-entrant phase transitions observed in ferromagnetic case

Critical exponents vary continuously, supporting weak universality

Quantum critical point at isotropic Heisenberg interaction

Abstract

The spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction and quartic Ising interactions is exactly solved by establishing a precise mapping relationship with the corresponding zero-field (symmetric) eight-vertex model. It is shown that the Ising-Heisenberg model with the ferromagnetic Heisenberg interaction exhibits a striking critical behavior, which manifests itself through re-entrant phase transitions as well as continuously varying critical exponents. The changes of critical exponents are in accordance with the weak universality hypothesis in spite of a peculiar singular behavior to emerge at a quantum critical point of the infinite order, which occurs at the isotropic limit of the Heisenberg interaction. On the other hand, the Ising-Heisenberg model with the antiferromagnetic Heisenberg interaction surprisingly exhibits less significant changes of both critical temperatures as well as critical exponents upon varying a strength of the exchange anisotropy in the Heisenberg interaction.