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Coherence and Uniqueness Theorems for Averaging Processes in Statistical Mechanics

Coherence and Uniqueness Theorems for Averaging Processes in Statistical Mechanics Let S be the set of scalings {n −1:n=1,2,3,...} and let L z =z Z 2, z∈S, be the corresponding set of scaled lattices in R 2. In this paper averaging operators are defined for plaquette functions on L z to plaquette functions on L z′ for all z′, z∈S, z′=dz, d∈{2,3,4,...}, 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=1,2,3,... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Coherence and Uniqueness Theorems for Averaging Processes in Statistical Mechanics

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References (14)

Publisher
Springer Journals
Copyright
Copyright © 2003 by Kluwer Academic Publishers
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1023/A:1024018909120
Publisher site
See Article on Publisher Site

Abstract

Let S be the set of scalings {n −1:n=1,2,3,...} and let L z =z Z 2, z∈S, be the corresponding set of scaled lattices in R 2. In this paper averaging operators are defined for plaquette functions on L z to plaquette functions on L z′ for all z′, z∈S, z′=dz, d∈{2,3,4,...}, 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=1,2,3,... 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.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Oct 5, 2004

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