Melting of Three-Sublattice Order in Easy-Axis Antiferromagnets on Triangular and Kagome Lattices

When the constituent spins have an energetic preference to lie along an easy axis, triangular and kagome lattice antiferromagnets often develop long-range order that distinguishes the three sublattices of the underlying triangular Bravais lattice. In zero magnetic field, this three-sublattice order melts either in a two-step manner, i.e., via an intermediate phase with power-law three-sublattice order controlled by a temperature-dependent exponent η(T)∈(1/9,1/4), or via a transition in the three-state Potts universality class. Here, I predict that the uniform susceptibility to a small easy-axis field B diverges as χ(B)∼|B|^{-[(4-18η)/(4-9η)]} in a large part of the intermediate power-law ordered phase [corresponding to η(T)∈(1/9,2/9)], providing an easy-to-measure thermodynamic signature of two-step melting. I also show that these two melting scenarios can be generically connected via an intervening multicritical point and obtain numerical estimates of multicritical exponents.