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

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.

Accepted version for PRB; 23 pages (16 main text), 20 figures

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Cited by in corpus (13)

• Tensor network approach to the fully frustrated XY model on a kagome lattice with a fractional vortex-antivortex pairing transition
• Unified tensor network theory for frustrated classical spin models in two dimensions
• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices
• Engineering frustrated Rydberg spin models by graphical Floquet modulation
• Magnetic properties and field-induced phenomena in the Jeff = 1/2 distorted kagome antiferromagnet
• Classical and quantum spin liquids
• Partial magnetic order in kagome spin ice
• Ergodic Archimedean dimers
• Spin Hamiltonians in the Modulated Momenta of Light
• Efficient optimization of variational tensor-network approach to three-dimensional statistical systems
• Fragile magnetic order in metallic quasicrystals
• Equivalence of residual entropy of hexagonal and cubic ices from tensor network methods