Two dimensional XXZ-Ising model on square-hexagon lattice

Abstract

We study a two dimensional XXZ-Ising on square-hexagon (4-6) lattice with spin-1/2. The phase diagram of the ground state energy is discussed, shown two different ferrimagnetic states and two type of antiferromagnetic states, beside of a ferromagnetic state. To solve this model, it could be mapped into the eight-vertex model with union jack interaction term. Imposing exact solution condition we find the region where the XXZ-Ising model on 4-6 lattice have exact solutions with one free parameter, for symmetric eight-vertex model condition. In this sense we explore the properties of the system and analyze the competition of the interaction parameters providing the region where it has an exact solution. However the present model does not satisfy the \textit{free fermion} condition, unless for a trivial situation. Even so we are able to discuss their critical points region, when the exactly solvable condition is ignored.

5 pages, 5 figures

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• Phase diagram of the asymmetric tetrahedral Ising-Heisenberg chain
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Cited by in corpus (10)

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• Direct algebraic mapping transformation for decorated spin models
• Frustrated Ising model on the Cairo pentagonal lattice
• 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
• Phase transitions and magnetization of the mixed-spin Ising-Heisenberg double sawtooth frustrated ladder
• 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
• Geometrically frustrated Ising-Heisenberg spin model on expanded Kagomé lattice
• Spontaneous distortion in the spin-1/2 Ising-Heisenberg model on decorated planar lattices with a magnetoelastic coupling
• Emergence of quantum spin frustration in spin-1/2 Ising-Heisenberg model on a decorated honeycomb lattice