Dilute semi-infinite Potts model

(Received 24 August 1990, accepted 9 November 1990)

Abstract
The influence of bond-dilution (which is assumed both on the surface and in the bulk) on the phase transitions of a semi-infinite d-dimensional q-state Potts model is investigated. Phase diagrams and critical exponents have been calculated within an extension of Migdal's approch to disordered systems. We find that the percolation effects in a semi-infinite system are characterised by phase diagrams of striking similarity to that of the pure system. Indeed, for the three-dimensional cubic lattice we observe four different phase transitions, irrespective of the number of Potts state, which can be designated using the same known terminology, namely the ordinary, surface, extraordinary, and special phase transitions.