Antiferromagnetic sawtooth chain with Heisenberg and Ising bonds

TL;DR

This paper presents an exact solution for a mixed Heisenberg-Ising antiferromagnetic sawtooth chain, revealing detailed thermodynamic and ground state properties through transfer-matrix techniques.

Contribution

It provides the first exact analytical solution for this specific mixed interaction sawtooth chain model, including thermodynamics and phase diagram analysis.

Findings

Exact expressions for thermodynamic functions

Ground state phase diagram mapped out

Insights into antiferromagnetic interactions in sawtooth chains

Abstract

The sawtooth chain with pairs of $S=1/2$ spins interacting with $XXZ$-interactions placed on each second tooth is considered. All other interaction bonds are taken to be of Ising type. Exact statistical mechanical solution of the model within the direct transfer-matrix technique is obtained. The solution allows one to obtain exact analytic expressions for all thermodynamic functions of the model. Ground stated properties are also investigated, the corresponding ground state phase diagram is presented.