Recursion relations for the partition function of the two-dimensional Ising model

Details Recursion relations for the partition function of the two-dimensional Ising model Recursion relations for the partition function of the two-dimensional Ising model

2006-05-23

arxiv.org/abs/cond-mat/0605568v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, no figures

Scientific paper

The partition function of the two-dimensional Ising model on a square lattice with nearest-neighbour interactions and periodic boundary conditions is investigated. Kaufman [Phys. Rev. 76, 1232--1243 (1949)] gave a solution for this function consisting of four summands. The summands are rewritten as functions of a low-temperature expansion variable, resulting in polynomials with integer coefficients. Considering these polynomials for system sizes $2^m\times 2^n$ ($m,n\in\N$), a variety of recursion relations in $m,n$ are found. The recursions reveal a rich structure of the partition function and can be employed to render the computer algebra calculation of the microcanonical partition function more efficient.

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