Melting of three-sublattice order in triangular lattice Ising antiferromagnets: Power-law order, $Z_6$ parafermionic multicriticality, and weakly first order transitions

Abstract

The nature of the thermal melting process by which triangular-lattice Ising antiferromagnets lose their low-temperature ferrimagnetic three-sublattice order depends on the range of the interactions: It changes character when second and third neighbour ferromagnetic interactions become comparable to the nearest-neighbour antiferromagnetic coupling. We present a detailed numerical characterization of the corresponding threshold at which two-step melting of three-sublattice order gives way to a direct first-order transition at which this order is lost. The multicritical behaviour at this threshold is argued to be in the universality class of the $Z_6$ parafermion conformal field theory with central charge $c=5/4$. The presence of this multicritical threshold influences the melting behaviour and long-wavelength properties over a fairly large range of parameters, and at temperatures that are of the same order as the exchange interactions. It is therefore of potential experimental relevance in the context of easy-axis triangular lattice antiferromagnets that display such low temperature ordering.

References in corpus (11)

• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• Emergent Supersymmetry from Strongly Interacting Majorana Zero Modes
• Free parafermions
• Parafermionic conformal field theory on the lattice
• Magnetic charge and ordering in kagome spin ice
• Edge quantum criticality and emergent supersymmetry in topological phases
• A supersymmetric multicritical point in a model of lattice fermions
• Cluster Luttinger liquids and emergent supersymmetric conformal critical points in the one-dimensional soft-shoulder Hubbard model
• Realization of supersymmetry and its spontaneous breaking in quantum Hall edges
• Fate of the one-dimensional Ising quantum critical point coupled to a gapless boson
• On the phase diagram of the discrete $Z_6$ spin models

Cited by in corpus (1)

• Nematicity and fractional magnetization plateaus induced by spin-lattice coupling in the classical kagome-lattice Heisenberg antiferromagnet