Multi-field effective Hamiltonian theory

Abstract

Ideally one would like to analyse the properties of inhomogeneous fluids/Ising-like magnets (e.g., wetting of a fluid phase at a wall or confinement in thin film geometries) using a microscopic Hamiltonian H[ m], with m( r ) the local order-parameter (number density/magnetization). For many problems, however, this is too difficult and traditionally one has to introduce effective interfacial models based on a collective coordinate l( y ) measuring the position of the fluid interface. We review progress made in unifying these approaches using multi-field effective Hamiltonian theory which is a powerful new investigative tool. We emphasize: (i) a systematic method for recovering order-parameter correlations G( r 1, r 2) from collective coordinate theory, (ii) the role of coupled fluctuations at three dimensional wetting transitions leading to (a) an observable increment to the value of the wetting parameter at complete wetting and (b) an inflation of the mean field regime for local surface response functions at critical wetting, (iii) the derivation of new identities relating moments of G at different positions in the fluid, and (iv) the development of a linear response theory of fluid adsorption at a non-planar wall which predicts roughness-induced first-order wetting transitions. The relevance of these predictions for long-standing controversies surrounding Ising model simulation studies is discussed.