English

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

R2 v1 2026-07-22T10:20:11.198Z