We formulate an inhomogeneous generalization of the bond-cluster approach to deal with interfacial phenomena in q-state Potts models. We apply this formalism to the wetting by the disordered phase of the interface between two bulk phases. For the case q=4 we obtain the full interfacial profiles, provide an estimate for the wetting temperature and verify the predicted logarithmic divergence of the wetting layer.

Physica A
Theory of Biomolecular Matter

Paraskevaidis, C. E., Papatriantafillou, C., & Mulder, B. (2007). Interfacial wetting in the 4-state Potts model: a cluster approach. Physica A, 375, 537–545. doi:10.1016/j.physa.2006.09.021