Kronecker's Double Series and Exact Asymptotic Expansion for Free Models of Statistical Mechanics on Torus

Details Kronecker's Double Series and Exact Asymptotic Expansion for Free Models of Statistical Mechanics on Torus Kronecker's Double Series and Exact Asymptotic Expansion for Free Models of Statistical Mechanics on Torus

2001-02-26

arxiv.org/abs/cond-mat/0102470v3

J. Phys. A: Math. Gen. 35 (2002) 5543-5561

Physics

Condensed Matter

Statistical Mechanics

REVTeX, 22 pages, this is expanded version which includes exact asymptotic expansions of the free energy, the internal energy

Scientific paper

10.1088/0305-4470/35/27/302

For the free models of statistical mechanics on torus, exact asymptotic expansions of the free energy, the internal energy and the specific heat in the vicinity of the critical point are found. It is shown that there is direct relation between the terms of the expansion and the Kronecker's double series. The latter can be expressed in terms of the elliptic theta-functions in all orders of the asymptotic expansion.

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