Critical behaviour of thin films with quenched impurities

The critical behaviour of thin films containing quenched random impurities and inhomogeneities is investigated by the renormalization-group method to the one-loop order within the framework of the n-component phi(4)-model. Th e finite-size crossover in impure films has been considered on the basis of the fundamental relationship between the effective dimensionality D-eff an d the characteristic lengths of the system. The fixed points, their stabili ty properties and the critical exponents are obtained and analyzed, using a n <(epsilon)over tilde>=(4-D-eff)-expansion near the effective. spatial dim ensionality D-eff of the fluctuation modes in D-dimensional hyperslabs with two types of quenched impurities: point-like impurities with short-range: random correlations and extended (linear) impurities with infinite-range ra ndom correlations along the small-size spatial direction. The difference be tween the critical properties of infinite systems and films is demonstrated and investigated. A new critical exponent, describing the scaling properti es of the thickness of films with extended impurities has been derived and calculated. A special attention is paid to the critical behaviour of real i mpure films (D=3). (C) 1999 Published by Elsevier Science B.V. All rights r eserved.