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

2009/02/28 by Jozef Strečka, Jozef Strecka, Lucia Canova +2
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Antiferromagnetism #Condensed matter physics #Critical exponent #Critical phenomena #Ferromagnetism #Heisenberg model #Ising model #Mathematical physics #Phase transition #Physics #Quantum many-body systems #Quantum mechanics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.79.051103

published as Phys. Rev. E 79 (2009) 051103 · 11 pages, 9 figures

openalex publication_date 2009/05/06 · arxiv created 2009/08/20 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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 in critical exponents are in accordance with the weak universality hypothesis in spite of a peculiar singular behavior that emerges 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 in both critical temperatures and critical exponents upon varying the strength of the exchange anisotropy in the Heisenberg interaction.

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