Series expansions for lattice Green functions release_rev_093bd34d-267e-4a0e-b2b8-1fcf540b4213

by Z. Maassarani

Released as a article .

2000  

Abstract

Lattice Green functions appear in lattice gauge theories, in lattice models of statistical physics and in random walks. Here, space coordinates are treated as parameters and series expansions in the mass are obtained. The singular points in arbitrary dimensions are found. For odd dimensions these are branch points with half odd-integer exponents, while for even dimensions they are of the logarithmic type. The differential equations for one, two and three dimensions are derived, and the general form for arbitrary dimensions is indicated. Explicit series expressions are found in one and two dimensions. These series are hypergeometric functions. In three and higher dimensions the series are more complicated. Finally an algorithmic method by Vohwinkel, Luscher and Weisz is shown to generalize to arbitrary anisotropies and mass.
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Type  article
Stage   submitted
Date   2000-03-26
Version   v2
Language   en ?
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