Partial lifting of degeneracy in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mtext>−</mml:mtext><mml:msub><mml:mi>J</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mtext>−</mml:mtext><mml:msub><mml:mi>J</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> Ising antiferromagnet on the kagome lattice
Jeanne Colbois, Bram Vanhecke, Laurens Vanderstraeten, Andrew Smerald, Frank Verstraete, Frédéric Mila
Abstract
Motivated by dipolar-coupled artificial spin systems, we present a theoretical study of the classical ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{3}$ 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.