Field theoretical treatment of a three-spin interaction model on triangular lattice

Abstract

We provide an effective description of a triangular-lattice model with a three-spin interaction. On the basis of a symmetry consideration, we argue that a vector dual sine-Gordon field theory is relevant, and provides us a framework to analyze long-distance behaviors. In particular, we can characterize a criticality of an intermediate phase between the low- and high-temperature phases. Also, in comparison with a model on the Union Jack lattice, we explain that the sublattice symmetry of the triangular lattice plays a crucial role to exhibit a novel phase transition. Theoretical predictions obtained are then confirmed by numerical calculations.