Pedestrian Solution of the Two-Dimensional Ising Model

Details Pedestrian Solution of the Two-Dimensional Ising Model Pedestrian Solution of the Two-Dimensional Ising Model

2001-04-20

arxiv.org/abs/cond-mat/0104398v6

Physics

Condensed Matter

Statistical Mechanics

10 pages, 2 figures; eqs. (101) and (102) corrected, files for fig. 2 fixed, minor beautifications

Scientific paper

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.

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