The $p$-state clock model is studied, for general values of $p$, from simulations using a heat-bath single spin flipping Monte Carlo method, and a mapping of the corresponding spinlike configurations to a solid-on-solid growth model. The growth exponents are calculated. From the dynamics generated by this far from equilibrium kinetic roughening of the surface one is able to characterize the corresponding equilibrium magnetic properties of the original model, such as the high temperature Berezinskii-Koserlitz-Thouless (BKT) transitions, the low-temperature long-range ordered phase transitions, as well as the conventional second-order phase transitions. The present method suggests that for $p\ge 5$ the high-temperature phase transition is indeed a BKT one, whose value is the same as that for $p\to \infty$ ($XY$ model), while the low-temperature phase transition has a first-order character.

• Received 12 February 2010

DOI:https://doi.org/10.1103/PhysRevE.81.031130