Recursion relations for the partition function of the two-dimensional Ising model
| dc.creator | Kastner, Michael | |
| dc.date | 2006-05-23 | |
| dc.date.accessioned | 2026-07-07T07:09:08Z | |
| dc.date.available | 2026-07-07T07:09:08Z | |
| dc.description | 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. | |
| dc.description | 7 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0605568 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0605568 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110949 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Recursion relations for the partition function of the two-dimensional Ising model | |
| dc.type | text |