The critical temperatures of the Ising model can be obtained by considering the elementary cells of the corresponding lattice, namely the square lattice in two dimensions and the cube in three dimensions. The configurations in the statistical sum of a cell are divided into nondegenerate and degenerate cases. At the critical temperature of the infinite lattice the contributions of these two groups of configurations are assumed to be equal. This conjecture reproduces the exact Onsager result for two dimensions and the numerical result for the three-dimensional Ising lattices. Although this conjecture is not exact, it gives insight into the nature of the transitions.
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August 01 2003
The critical temperature of two-dimensional and three-dimensional Ising models
B. Liu, M. Gitterman; The critical temperature of two-dimensional and three-dimensional Ising models. Am. J. Phys. 1 August 2003; 71 (8): 806–808. https://doi.org/10.1119/1.1579495
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