Critical behaviour of thin films with quenched impurities

• Published in: Physica A Vol. 270; no. 3; pp. 486 - 513
• Main Authors: Craco, L., Cesare, L.De, Rabuffo, I., Takov, I.P., Uzunov, D.I.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.08.1999
• Subjects: Critical phenomena; Dimensional crossover; Finite size scaling; Phase transition; Quenched disorder; Renormalization group; Thin films; Thin films; Dimensional crossover; 64.60.Fr; 05.70.Jk; 68.35.Rh; Quenched disorder; Finite size scaling; Critical phenomena; 64.60.Ak; Phase transition; Renormalization group
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/S0378-4371(99)00101-6

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 φ 4 -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 ε ̃ =(4−D eff ) -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).