Partition Functions in Statistical Mechanics, Symmetric Functions, and Group Representations

Details Partition Functions in Statistical Mechanics, Symmetric Functions, and Group Representations Partition Functions in Statistical Mechanics, Symmetric Functions, and Group Representations

2001-09-06

arxiv.org/abs/cond-mat/0109112v1

Phys.Rev. E64 (2001) 066105

Physics

Condensed Matter

Statistical Mechanics

16 pages of RevTex

Scientific paper

10.1103/PhysRevE.64.066105

Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation of the partition functions for particles that carry internal quantum numbers. The partition function is shown to be a sum of one or more group characters. The utility of character expansions in calculating the partition functions is explored. Several examples are given to illustrate these techniques.

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