Pedestrian Solution of the Two-Dimensional Ising Model
Statistical Mechanics
2013-05-29 v6
Abstract
The partition function of the two-dimensional Ising model with zero magnetic field on a square lattice with m x n sites wrapped on a torus is computed within the transfer matrix formalism in an explicit step-by-step approach inspired by Kaufman's work. However, working with two commuting representations of the complex rotation group SO(2n,C) helps us avoid a number of unnecessary complications. We find all eigenvalues of the transfer matrix and therefore the partition function in a straightforward way.
Keywords
Cite
@article{arxiv.cond-mat/0104398,
title = {Pedestrian Solution of the Two-Dimensional Ising Model},
author = {Boris Kastening},
journal= {arXiv preprint arXiv:cond-mat/0104398},
year = {2013}
}
Comments
10 pages, 2 figures; eqs. (101) and (102) corrected, files for fig. 2 fixed, minor beautifications