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

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.

11 pages, 9 figures

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Cited by in corpus (8)

• Generalized algebraic transformations and exactly solvable classical-quantum models
• Direct algebraic mapping transformation for decorated spin models
• Correlation functions in one-dimensional spin lattices with Ising and Heisenberg bonds
• Exact evidence for the spontaneous antiferromagnetic long-range order in the two-dimensional hybrid model of localized Ising spins and itinerant electrons
• Spinless fermion model on diamond chain
• Ferromagnetic Heisenberg model with the Dzyaloshinskii-Moriya interaction
• Spontaneous distortion in the spin-1/2 Ising-Heisenberg model on decorated planar lattices with a magnetoelastic coupling
• Quantum decoration transformation for spin models