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 φ⁴-model. The finite-size crossover in impure films has been considered on the basis of the fundamental relationship between the effective dimensionality D_eff and the characteristic lengths of the system. The fixed points, their stability properties and the critical exponents are obtained and analyzed, using an -expansion near the effective spatial dimensionality 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 random correlations along the small-size spatial direction. The difference between the critical properties of infinite systems and films is demonstrated and investigated. A new critical exponent, describing the scaling properties of the thickness of films with extended impurities has been derived and calculated. A special attention is paid to the critical behaviour of real impure films (D=3).