Two dimensional XXZ-Ising model on square-hexagon lattice

TL;DR

This paper investigates the ground state phase diagram of a two-dimensional XXZ-Ising model on a square-hexagon lattice, identifying various magnetic states and conditions for exact solvability via mapping to the eight-vertex model.

Contribution

It introduces an exact solution framework for the XXZ-Ising model on a 4-6 lattice by mapping to the eight-vertex model and explores the system's phase diagram and critical points.

Findings

Identifies ferrimagnetic and antiferromagnetic phases.

Derives conditions for exact solutions with one free parameter.

Analyzes critical points when exact solvability conditions are relaxed.

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.