Classification of continuous order-disorder transitions in adsorbed monolayers

Abstract

We present a classification of continuous order-disorder transitions of an adsorbed monolayer on substrates with $P2\mathrm{mm}$, $C2\mathrm{mm}$, $P4\mathrm{mm}$, and $P6\mathrm{mm}$ symmetries, assuming the validity of the Landau-Lifshitz theory (apart from the rule against third-order invariants). The transitions belong to the universality class of the Ising, three- or four-state Potts model, and $X-Y$ model with "cubic" anisotropy.