Local Functional Models of Critical Correlations in Thin Films

Recent work on local functional theories of critical inhomogeneous fluids and Ising-like magnets has shown them to be a potentially exact, or near exact, description of universal finite-size effects associated with the excess free energy and scaling of one-point functions in critical thin films. This approach is extended to predict the two-point correlation function G in critical thin films with symmetric surface fields in arbitrary dimension d. In d = 2 we show there is exact agreement with the predictions of conformal invariance for the complete spectrum of correlation lengths ξ⁽ⁿ⁾ as well as the detailed position dependence of the asymptotic decay of G. In d = 3 and d≥4 we present new numerical predictions for the universal finite-size correlation length and scaling functions determining the structure of G across the thin film. Highly accurate analytical closed form expressions for these universal properties are derived in arbitrary dimension.