Wetting in Potts and Blume-Capel Models

Wetting may occur when three or more phases (A, B, C,...) coexist. It consists of the appearance of a thick (macroscopic) layer of the C phase at an interface between the A and the B phases. This phenomenon has been observed experimentally and in computer simulation (for a review, see Ref. 1). It has also been investigated by mean field theory ~2 4) and by lowtemperature expansions. (s'6) In this note we use the method of low-temperature expansions (7'8) to analyze the wetting of two ordered phases by the disordered one in the q-state Potts model, for q large. We first review low-temperature expansions in a simple example: the (generalized) Blume Capel model. There we make explicit the connection between these expansions and the rigorous Pirogov-Sinai theory of first-order phase transition. (7'9) We argue that the Potts model, at the transition temperature where ordered and disordered states coexist, is very similar, for large q, to the Blume-Capel model at low temperatures. Then we carry out for the