Ising antiferromagnet on the 2-uniform lattices

TL;DR

This study systematically explores the antiferromagnetic Ising model on 20 2-uniform lattices, revealing new phases like partial long-range order and partial spin ice, but not finding a spin liquid ground state.

Contribution

It provides a comprehensive analysis of geometric frustration effects on 2-uniform lattices using Monte Carlo methods, discovering novel phases beyond known Archimedean lattice behaviors.

Findings

Identified partial long-range order with residual entropy.

Discovered partial spin ice phase with partial freezing.

Did not find spin liquid ground state in 2-uniform lattices.

Abstract

The antiferromagnetic Ising model is investigated on the 20 2-uniform lattices using the Monte-Carlo method based on the Wang-Landau algorithm and the Metropolis algorithm to study the geometric frustration effect systematically. Based on the specific heat, the residual entropy, and the Edwards-Anderson freezing order parameter, the ground states of them were determined. In addition to the long-range-ordered phase and the spin ice phase found in the Archimedean lattices, two more phases were found. The partial long-range order is long-range order with exceptional disordered sites, which gives extensive residual entropy. In the partial spin ice phase, the partial freezing phenomenon appears: Majority of sites are frozen without long-range order, but the other sites are fluctuating even at zero temperature. The spin liquid ground state was not found in the 2-uniform lattices.