Phase boundaries of the isotropic helical Potts model on a square lattice

Abstract

The helical Potts model, a generalization of the $q$-state Potts model relevant to the commensurate-incommensurate transition, is studied on the square lattice. Close to zero temperature this model can be mapped onto the six-vertex Baxter model in direct fields. This mapping indicates the presence of an incommensurate phase, characterized by algebraic decay of correlations with an exponent $\eta \to \frac{3}{q^2}$ as $T\to 0$. A Lifshitz-like point occurs when the ferromagnetic, modulated, and disordered phases meet.