Antiferromagnetic Ising model saturation field entropies: ladders and kagome lattice

TL;DR

This paper calculates the saturation field entropies of antiferromagnetic Ising models on ladders and the kagome lattice, providing exact results and insights relevant to spin-ice materials.

Contribution

It presents exact calculations of saturation field entropies for specific lattices and applies an efficient algorithm to a large kagome lattice, linking theory to experiments.

Findings

Exact entropy for ladders via transfer matrices

Entropy for kagome lattice: S = 0.393589(6)

Relevance to spin-ice compound dysprosium titanium oxide

Abstract

Saturation field entropies of antiferromagnetic Ising models on quasi one-dimensional lattices (ladders) and the kagome lattice are calculated. The former is evaluated exactly by constructing the corresponding transfer matrices, while the latter calculation uses Binder's algorithm for efficiently and exactly computing the partition function of over 1300 spins to give, in Boltzmann's units, S = 0.393589(6). We comment on the relation of the kagome lattice to the experimental situation in the spin-ice compound dysprosium titanium oxide.