Universal and non-universal short-distance expansions in the strong, weak and intermediate fluctuation regimes of critical wetting

Abstract

The author studies the scaling properties of the density profile rho (z) of a fluid near a wall undergoing a critical wetting transition in the strong-fluctuation and in the weak-fluctuation scaling regimes. A critical exponent theta describing the short-distance algebraic decay of the density profile (for distances z normal to the wall much less than the perpendicular correlation length zeta perpendicular to ) is calculated explicitly in dimension d=2 using an effective interfacial Hamiltonian model. The exponent theta is found to be universal in the strong-fluctuation regime ( theta =1) and in the weak-fluctuation regime ( theta =3). In contrast to the other standard critical exponents theta is non-universal at the weak-fluctuation/mean-field borderline. The author discusses the origin of the universality of theta in the different fluctuation regimes and derives expressions for theta , valid for general d, in terms of known critical exponents.