Melting of three-sublattice order in easy-axis antiferromagnets on triangular and Kagome lattices

TL;DR

This paper predicts how three-sublattice order in easy-axis antiferromagnets on triangular and Kagome lattices melts, revealing a divergence in susceptibility and connecting different melting scenarios through a multicritical point.

Contribution

It introduces a theoretical prediction for susceptibility divergence during two-step melting and explores the connection between different melting scenarios via multicritical points.

Findings

Susceptibility diverges as |B|^{-(4 - 18 η)/(4-9η)} in the intermediate phase.

Two melting scenarios are connected through a multicritical point.

Numerical estimates of multicritical exponents are provided.

Abstract

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 {\em either} in a two-step manner, {\em i.e.} via an intermediate phase with power-law three-sublattice order controlled by a temperature dependent exponent $\eta(T) \in (\frac{1}{9},\frac{1}{4})$, {\em 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 $\chi(B) \sim |B|^{-\frac{4 - 18 \eta}{4-9\eta}}$ in a large part of the intermediate power-law ordered phase (corresponding to $\eta(T) \in (\frac{1}{9},\frac{2}{9})$), 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.