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The Kac-Ward solution of the 2D Ising model

The Ising model was originally introduced as a model for ferromagnetism but it has found wider applicability. I will review the setting, and the elegant, exact solution to the two-dimensional model by Kac and Ward. A well-known consequence is that the specific heat has logarithmic singularity at the critical temperature.

Recently, Cimasoni, Duminil-Copin, and Li found an equation for the critical temperature for general bi-periodic planar lattices. It is proved only for positive coupling constants, but we observe that it is valid more generally.

Joint work with Georgios Athanasopoulos.