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Pedestrian Solution of the Two-Dimensional Ising Model

Boris Kastening
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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.

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Boris Kastening. 2005-05-02. Pedestrian Solution of the Two-Dimensional Ising Model. https://doi.org/10.1103/physreve.64.066106

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