Some exactly solvable and tunable frustrated spin models

TL;DR

This paper introduces three exactly solvable models of geometric frustration in spin systems, including vertex, frustrated Ising, and spin ice models, providing new insights into their solvability and properties.

Contribution

It presents three novel exactly solvable frustrated spin models, expanding the understanding of solvable cases in geometric frustration.

Findings

Mapped a vertex model to a planar Ising model

Interpolated between Onsager's and Villain's frustrated models

Solved spin ice models on a tree using recursion

Abstract

We discuss three exactly solvable spin models of geometric frustration. First, we discuss a 1-parameter subfamily of the 16 vertex model, which can be mapped to a planar Ising model and solved via Fisher-Dubed\'{a}t decorations. We then consider a 1-parameter family generalization of the Villain's fully frustrated model, which interpolates between Onsager's 2D Ising model and the Villain one. We then discuss spin ice models on a tree, which can be solved exactly using recursions \textit{a l\'{a} Bethe}.