Comment on `Equilibrium crystal shape of the Potts model at the first-order transition point'

TL;DR

This paper confirms and provides an alternative derivation of the exact equilibrium crystal shape in the critical Q-state Potts model, demonstrating its equivalence with the Ising model through transformation properties of the six-vertex model.

Contribution

It offers an alternative derivation of the ECS in the Potts model, linking it to the Ising model via the six-vertex model's dispersion relation.

Findings

Confirmed the ECS in the Potts model matches that of the Ising model.

Derived the ECS using transformation properties of the six-vertex model.

Established the equivalence of dispersion relations between models.

Abstract

We comment on the article by Fujimoto (1997 J. Phys. A: Math. Gen., Vol. 30, 3779), where the exact equilibrium crystal shape (ECS) in the critical Q-state Potts model on the square lattice was calculated, and its equivalence with ECS in the Ising model was established. We confirm these results, giving their alternative derivation applying the transformation properties of the one-particle dispersion relation in the six-vertex model. It is shown, that this dispersion relation is identical with that in the Ising model on the square lattice.