Critical behaviour of thin films with quenched impurities

Abstract

The critical behaviour of thin films containing quenched random impurities and inhomogeneities is investigated by the renormalization-group method. The finite-size crossover in impure films has been considered on the basis of the fundamental relationship between the effective spatial dimensionality and the characteristic lengths of the system. 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 deduced and calculated. A special attention is paid to the critical behaviour of real impure films.Comment: 27 pages LaTex; figures are available in the journal varian

Some basic aspects of quantum phase transitions

“…The method used in Ref. [182] confirms this properties but the attempt to obtain an analytical dependence δ(y) have not been successful. Moreover, the method does not provide a sufficient accuracy of the results for the intermediate values y ∼ 1 correspondong to δ ∼ 0.5.…”

“…So, the strongly correlated along the small size point impurities behave like continuous uniform strings. In regard to the critical behaviour this disorder acts like point impurities with a short-range random distribution along the large (infinite) dimensions L i and an uniform distribution along the small size L 0 [182].…”

“…7.4-7.5 have been used in Ref. [182] in the study of disordered thin films with quenched point and extended (line) impurities. The method of work is similar to the Weichman-Kim [190] and Schakel [115] methods.…”

“…[182] the δ−integration as a method of calculation of perturbation terms introduces a systematic error of a finite magnitude, except for the limiting cases δ = 0, 1. While the RG studies are related with infrared divergences this finite error produces only incorrect values of the FP coordinates but does not affect the physically measurable quantities as the critical exponents.…”

“…(29) for σ = 2, m = 2, and m ′ = 0. This correspondence is valid for both pure [70] and impure films [182], and is given by the formal replacement of the film thickness L 0 with 1/T .…”