Partition functions in statistical mechanics, symmetric functions, and group representations

The symmetric group - representations, combinatorial algorithms, and symmetric functions

Partition Functions for Statistical Mechanics with Micropartitions and Phase Transitions

X iv :c on dm at /0 41 11 76 v1 [ co nd -m at .s ta tm ec h] 7 N ov 2 00 4 PARTITION FUNCTIONS FOR STATISTICAL MECHANICS WITH MICROPARTITIONS AND PHASE TRANSITIONS AJAY PATWARDHAN Physics department, St Xavier’s college, Mahapalika Marg , Mumbai 400001,India Visitor, Institute of Mathematical Sciences, CIT campus, Tharamani, Chennai, India [email protected] ABSTRACT The fundamentals of Statistic...

Partition functions and symmetric polynomials

We find a close correspondence between certain partition functions of ideal quantum gases and certain symmetric polynomials. Due to this correspondence it can be shown that a number of thermodynamic identities which have recently been considered are essentially of combinatorical origin and known for a long time as theorems on symmetric polynomials. For example, a recurrence relation for partiti...

Alcove walks, buildings, symmetric functions and representations

For a complex simple Lie algebra g, the dimension Kλμ of the μ weight space of a finite dimensional representation of highest weight λ is the same as the number of Littelmann paths of type λ and weight μ. In this paper we give an explicit construction of a path of type λ and weight μ whenever Kλμ 6= 0. This construction has additional consequences, it produces an explicit point in the building ...

Renormalization group in Statistical Mechanics and Mechanics: gauge symmetries and vanishing beta functions

Two very different problems that can be studied by renormalization group methods are discussed with the aim of showing the conceptual unity that renormalization group has introduced in some areas of theoretical Physics. The two problems are: the ground state theory of a one dimensional quantum Fermi liquid and the existence of quasi periodic motions in classical mechanical systems close to inte...