Kronecker$apos$s double series and exact asymptotic expansions for free models of statistical mechanics on torus
- 28 June 2002
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 35 (27) , 5543-5561
- https://doi.org/10.1088/0305-4470/35/27/302
Abstract
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.Keywords
All Related Versions
This publication has 13 references indexed in Scilit:
- Exact amplitude ratio and finite-size corrections for thesquare lattice Ising modelPhysical Review E, 2002
- Exact Universal Amplitude Ratios for Two-Dimensional Ising Models and a Quantum Spin ChainPhysical Review Letters, 2001
- Exact finite-size-scaling corrections to the critical two-dimensional Ising model on a torusJournal of Physics A: General Physics, 2001
- Geometry, thermodynamics, and finite-size corrections in the critical Potts modelPhysical Review E, 1999
- Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts ModelJournal of Statistical Physics, 1997
- Bounded and Inhomogeneous Ising Models. I. Specific-Heat Anomaly of a Finite LatticePhysical Review B, 1969
- Statistical Mechanics of Dimers on a Plane LatticePhysical Review B, 1961
- The statistics of dimers on a latticePhysica, 1961
- Crystal Statistics. II. Partition Function Evaluated by Spinor AnalysisPhysical Review B, 1949
- Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder TransitionPhysical Review B, 1944