Partial lifting of degeneracy in the $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice

TL;DR

This paper investigates the phase diagram and entropy of the classical $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice, revealing partial degeneracy lifting and complex ground-state competition.

Contribution

It provides the first detailed phase diagram for the model with exact ground-state energies and accurate entropy calculations using tensor networks, highlighting new degeneracy and competition phenomena.

Findings

Three macroscopically degenerate ground-state phases identified.

Entropies of phases are fractions of the triangular lattice case.

Dipolar ground state is favored at smaller $J_3$ interactions.

Abstract

Motivated by dipolar-coupled artificial spin systems, we present a theoretical study of the classical $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice. We establish the ground-state phase diagram of this model for $J_1 > |J_2|, |J_3|$ based on exact results for the ground-state energies. When all the couplings are antiferromagnetic, the model has three macroscopically degenerate ground-state phases, and using tensor networks, we can calculate the entropies of these phases and of their boundaries very accurately. In two cases, the entropy appears to be a fraction of that of the triangular lattice Ising antiferromagnet, and we provide analytical arguments to support this observation. We also notice that, surprisingly enough, the dipolar ground state is not a ground state of the truncated model, but of the model with smaller $J_3$ interactions, an indication of a very strong competition between low-energy states in this model.