Local functional models of critical correlations in thin films

Recent work on local functional theories of critical inhomogeneous fluids a nd Ising-like magnets has shown them to be a potentially exact, or near exa ct, description of universal finite-size effects associated with the excess free energy and scaling of one-point functions in critical thin films. Thi s approach is extended to predict the two-point correlation function G in c ritical thin films with symmetric surface fields in arbitrary dimension d. Tn d = 2 we show there is exact agreement with the predictions of conformal invariance for the complete spectrum of correlation lengths xi ((n)) as we ll as the detailed position dependence of the asymptotic decay of G. In d = 3 and d greater than or equal to 4 we present new numerical predictions fo r the universal finite-size correlation length and scaling functions determ ining the structure of G across the thin film. Highly accurate analytical c losed form expressions for these universal properties are derived in arbitr ary dimension.