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arXiv:cond-mat/0509720 · Physica A Statistical Mechanics and its Applications

Critical behaviour of thin films with quenched impurities

L. Craco, L.De Cesare, I. Rabuffo, I.P. Takov, D.I. Uzunov

Published Aug 1, 1999• 9 citations
arXivHTMLPDF
DOI
10.1016/s0378-4371(99)00101-6

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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 Deff and the characteristic lengths of the system. The fixed points, their stability properties and the critical exponents are obtained and analyzed, using an ε̃=(4−Deff)-expansion near the effective spatial dimensionality Deff 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).
By means of the renormalisation-group approach, static and dynamic critical behaviours are studied for the XY spin system with cubic anisotropy and with quenched random nonmagnetic impurities. The stability of the quenched-random-impurity fixed point in d ( identical to 4- epsilon ) dimensions, the flow diagram of the interactions and the critical exponents are investigated, within the two-loop approximation, in terms of the epsilon 1/2 expansion. It is shown that the transition that appears is a first-order transition.