Solving the Functional Schroedinger Equation: Yang-Mills String Tension and Surface Critical Scaling

Motivated by a heuristic model of the Yang-Mills vacuum that accurately describes the string-tension in three dimensions we develop a systematic method for solving the functional Schroedinger equation in a derivative expansion. This is applied to the Landau-Ginzburg theory that describes surface critical scaling in the Ising model. A Renormalisation Group analysis of the solution yields the value eta=1.003 for the anomalous dimension of the correlation function of surface spins which compares well with the exact result of unity implied by Onsager’s solution. We give the expansion of the corresponding beta-function to 17-th order (which receives contributions from up to 17-loops in conventional perturbation theory).