Coherence and uniqueness theorems for averaging processes in statistical mechanics

Details Coherence and uniqueness theorems for averaging processes in statistical mechanics Coherence and uniqueness theorems for averaging processes in statistical mechanics

2004-10-21

arxiv.org/abs/math-ph/0410046v1

Acta Appl. Math. 77 (2003), 105-123

Physics

Mathematical Physics

18 pages, 4 figures

Scientific paper

Let S be the set of scalings 1, 2,3,4, ... and consider the corresponding set of scaled lattices in the plane. In this paper averaging operators are defined for plaquette functions on a lattice to plaquette functions on a coarser lattice for all scale factors and their coherence is proved. This generalizes the averaging operators introduced by Balaban and Federbush. There are such coherent families of averaging operators for any dimension D and not only for D=2. Finally there are uniqueness theorems saying that in a sense, besides a form of straightforward averaging, the weights used are the only ones that give coherent families of averaging operators.

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