Internal Energy of the Potts model on the Triangular Lattice with Two- and Three-body Interactions

TL;DR

This paper computes the internal energy of the Potts model on a triangular lattice with complex interactions at the phase transition point using duality transformations, supported by numerical verification for specific cases.

Contribution

It introduces a duality-based method to calculate the internal energy at transition points for the Potts model with multi-body interactions, assuming second-order transitions.

Findings

Results are exact for q=2, 3, 4 based on numerical verification.

Method applies duality transformations to complex lattice models.

Provides insights into phase transition properties of the Potts model.

Abstract

We calculate the internal energy of the Potts model on the triangular lattice with two- and three-body interactions at the transition point satisfying certain conditions for coupling constants. The method is a duality transformation. Therefore we have to make assumptions on uniqueness of the transition point and that the transition is of second order. These assumptions have been verified to hold by numerical simulations for q=2, 3 and 4, and our results for the internal energy are expected to be exact in these cases.