On the Mutual Cancellation of Cluster Integrals in Mayer's Fugacity Series
H. Temperley. Proceedings of the Physical Society, 83 (1):
3--16(1964)
Abstract
Theorems are proved for each of two models representing purely repulsive interactions, the `Gaussian' and the `rigid line'. In both cases we study the fugacity series by starting with the complete diagram of l points connected by ½ l ( l -1) lines. For the Gaussian model, it is proved rigorously that the cluster integral corresponding to any diagram can be expressed as a product , each disjoint set of lines in the complementary diagram contributing one factor . The result for the `rigid-line' model is that any cluster integral can be expressed as a sum , each disjoint set of lines in the complementary diagram contributing a term , with corresponding results for the `rigid-square' and `rigid-cube' models. These results enable the consequences of the `Gaussian' model to be worked out almost completely, and provide some justification for approximate treatments that neglect all but the more `open' diagrams. The `rigid-square' model is more difficult analytically, and only a few preliminary deductions have been made.
%0 Journal Article
%1 temperley64
%A Temperley, H. N. V.
%D 1964
%J Proceedings of the Physical Society
%K effective.resistance graph.theory laplacian network resistor spanning tree
%N 1
%P 3--16
%T On the Mutual Cancellation of Cluster Integrals in Mayer's Fugacity Series
%U http://stacks.iop.org/0370-1328/83/i=1/a=302
%V 83
%X Theorems are proved for each of two models representing purely repulsive interactions, the `Gaussian' and the `rigid line'. In both cases we study the fugacity series by starting with the complete diagram of l points connected by ½ l ( l -1) lines. For the Gaussian model, it is proved rigorously that the cluster integral corresponding to any diagram can be expressed as a product , each disjoint set of lines in the complementary diagram contributing one factor . The result for the `rigid-line' model is that any cluster integral can be expressed as a sum , each disjoint set of lines in the complementary diagram contributing a term , with corresponding results for the `rigid-square' and `rigid-cube' models. These results enable the consequences of the `Gaussian' model to be worked out almost completely, and provide some justification for approximate treatments that neglect all but the more `open' diagrams. The `rigid-square' model is more difficult analytically, and only a few preliminary deductions have been made.
@article{temperley64,
abstract = {Theorems are proved for each of two models representing purely repulsive interactions, the `Gaussian' and the `rigid line'. In both cases we study the fugacity series by starting with the complete diagram of l points connected by ½ l ( l -1) lines. For the Gaussian model, it is proved rigorously that the cluster integral corresponding to any diagram can be expressed as a product , each disjoint set of lines in the complementary diagram contributing one factor . The result for the `rigid-line' model is that any cluster integral can be expressed as a sum , each disjoint set of lines in the complementary diagram contributing a term , with corresponding results for the `rigid-square' and `rigid-cube' models. These results enable the consequences of the `Gaussian' model to be worked out almost completely, and provide some justification for approximate treatments that neglect all but the more `open' diagrams. The `rigid-square' model is more difficult analytically, and only a few preliminary deductions have been made.},
added-at = {2016-05-11T15:08:58.000+0200},
author = {Temperley, H. N. V.},
biburl = {https://www.bibsonomy.org/bibtex/2ebfab88ac1209f631fea0a4b36b56115/ytyoun},
interhash = {f0f54fde2cab88ca0082d6656a01541e},
intrahash = {ebfab88ac1209f631fea0a4b36b56115},
journal = {Proceedings of the Physical Society},
keywords = {effective.resistance graph.theory laplacian network resistor spanning tree},
number = 1,
pages = {3--16},
timestamp = {2016-05-11T15:19:53.000+0200},
title = {On the Mutual Cancellation of Cluster Integrals in {Mayer's} Fugacity Series},
url = {http://stacks.iop.org/0370-1328/83/i=1/a=302},
volume = 83,
year = 1964
}