Effective Field Theory of Triangular-Lattice Three-Spin Interaction Model

TL;DR

This paper develops an effective field theory for a triangular-lattice three-spin interaction model with ${f Z}_p$ variables, showing that the vector dual sine-Gordon model captures its long-distance behavior for $p extgreater=5$ and supporting this with numerical transfer matrix analysis.

Contribution

It introduces a vector dual sine-Gordon model to describe the critical properties of the ${f Z}_p$ triangular-lattice three-spin interaction model for $p extgreater=5$, linking symmetry and ideal-state graph concepts.

Findings

The vector dual sine-Gordon model accurately describes the model's long-distance physics for $p extgreater=5$.

Numerical analysis confirms the criticality with central charge $c=2$ for $p=6$.

The eigenvalue structure of the transfer matrix supports the theoretical predictions.

Abstract

We discuss an effective field theory of a triangular-lattice three-spin interaction model defined by the ${\mathbb Z}_p$ variables. Based on the symmetry properties and the ideal-state graph concept, we show that the vector dual sine-Gordon model describes the long-distance properties for $p\ge5$; we then compare its predictions with the previous argument. To provide the evidences, we numerically analyze the eigenvalue structure of the transfer matrix for $p=6$, and we check the criticality with the central charge $c=2$ of the intermediate phase and the quantization condition of the vector charges.