Interface wandering in adsorbed and bulk phases, pure and impure

Abstract

After brief mention of recent experiments on phase transitions in adsorbed and surface layers which confirm detailed predictions of the theory of planar Ising models, the statistical mechanics of interfaces in d= 2,3, and more bulk dimensions is addressed for both pure and impure systems. The existence of various interface types in two-dimensional ordered layers is explained and the significance of the associated wetting transitions for commensurate melting is mentioned. The general theory is then developed systematically on the basis of the wandering or roughening exponent, ζ(d), which determines the scale, L_⊥, of transverse fluctuations of an interface segment of longitudinal length scale, L_∥, viaL_⊥≃L^ζ_∥. In terms of ζ, one can understand heuristically wall–interface and interface–interface interactions, and thence obtain the critical exponents describing commensurate–incommensurate transitions, complete wetting behaviour, and critical wetting transitions, including the effects of long-range van der Waals forces. The well known value, ½(3–d), of ζ(d) for thermally driven interface fluctuations and recent results for quenched random media with random-field, ζ=⅓(5–d), or random-bond disorder, then yield a variety of concrete predictions, several already checked by exact model calculations, most representing open experimental challenges.