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

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

2004-06-25

arxiv.org/abs/hep-th/0406237v1

JHEP0404:059,2004

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, 7 Postscript figures

Scientific paper

10.1088/1126-6708/2004/04/059

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).

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