Canonical Partition Functions for Parastatistical Systems of any order

TL;DR

This paper derives a general formula for the canonical partition function of systems obeying permutation-based parastatistics, unifying previous results and elucidating Fock space structures.

Contribution

It introduces a comprehensive formula for parastatistical partition functions using Schur functions, extending prior specific cases to any order.

Findings

Unified formula for parastatistical partition functions

Special case of order two matches previous results

Provides insights into Fock space structures for parasystems

Abstract

A general formula for the canonical partition function for a system obeying any statistics based on the permutation group is derived. The formula expresses the canonical partition function in terms of sums of Schur functions. The only hitherto known result due to Suranyi [ Phys. Rev. Lett. {\bf 65}, 2329 (1990)] for parasystems of order two is shown to arise as a special case of our general formula. Our results also yield all the relevant information about the structure of the Fock spaces for parasystems.