Ising antiferromagnet on the Archimedean lattices

TL;DR

This study systematically investigates geometric frustration in the Ising antiferromagnet on all 11 Archimedean lattices using Monte Carlo methods, revealing various ground states and phases.

Contribution

It provides the first comprehensive analysis of frustration effects and ground states across all Archimedean lattices with exact and numerical methods.

Findings

Exact residual entropy was determined.

Different lattices exhibit distinct phases like spin ice and spin liquid.

Ground states range from long-range order to disordered phases.

Abstract

Geometric frustration effects were studied systematically with the Ising antiferromagnet on the 11 Archimedean lattices using the Monte-Carlo methods. The Wang-Landau algorithm for static properties (specific heat and residual entropy) and the Metropolis algorithm for a freezing order parameter were adopted. The exact residual entropy was also found. Based on the degree of frustration and dynamic properties, ground states of them were determined. The Shastry-Sutherland lattice and the trellis lattice are weakly-frustrated and have two-dimensional and one-dimensional long-range-ordered ground states, respectively. The bounce, maple-leaf, and star lattices have the spin ice phase. The spin liquid phase appears in the triangular and kagom\'e lattices.