Partial lifting of degeneracy in the J₁-J₂-J₃ Ising antiferromagnet on the kagome lattice

Motivated by dipolar-coupled artificial spin systems, we present a theoretical study of the classical J1-J2-J3 Ising antiferromagnet on the kagome lattice. We establish the ground-state phase diagram of this model for J1>|J2|,|J3| 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 J3 interactions, an indication of a very strong competition between low-energy states in this model.