Antiferromagnetic Ising model on the sorrel net: a new frustrated corner-shared triangle lattice

TL;DR

This paper investigates the antiferromagnetic Ising model on a novel sorrel net lattice, revealing high frustration, residual entropy, and complex magnetic ordering influenced by bond depletion and interactions.

Contribution

It introduces the sorrel net lattice for the AFI model, providing new insights into frustration, residual entropy, and magnetic order in a partially depleted triangular lattice.

Findings

Residual entropy of 0.48185 per site indicating high frustration

Identification of long-range partial order for antiferromagnetic $J_2$

Crossover in magnetic susceptibility from Curie-Weiss to Curie law

Abstract

We study the antiferromagnetic classical Ising (AFI) model on the sorrel net, a 1/9th site depleted and 1/7th bond depleted triangular lattice. Our classical Monte Carlo simulations, verified by exact results for small system sizes, show that the AFI model on this corner-shared triangle net (with coupling constant $J_1$) is highly frustrated, with a residual entropy of $\frac{S}{N}$= 0.48185$\pm$0.00008. Anticipating that it may be difficult to achieve perfect bond depletion, we investigate the physics originating from turning back on the deleted bonds ($J_2$) to create a lattice of edge-sharing triangles. Below a critical temperature which grows linearly with $J_2$ for small $J_2$, we identify the nature of the unusual magnetic ordering and present analytic expressions for the low temperature residual entropy. We compute the static structure factor and find evidence for long range partial order for antiferromagnetic $J_2$, and short range magnetic order otherwise. The magnetic susceptibility crosses over from following a Curie-Weiss law at high temperatures to a low temperature Curie law whose slope clearly distinguishes ferromagnetic $J_2$ from the $J_2 = 0$ case. We briefly comment on a recent report of the creation of a 1/9th site depleted triangular lattice cobalt hydroxide oxalate.