Geodesic
Pfaffian and the Kac--Ward Formula in the Two-Dimensional Ising Model
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Nonlinear dynamics, Tome 251 (2005), pp. 139-153

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By using the Pfaffian method, we get a simple proof of the Kac–Ward formula for the two-dimensional Ising model with free boundary conditions. 
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     title = {Pfaffian and the {Kac--Ward} {Formula} in the {Two-Dimensional} {Ising} {Model}},
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Yu. M. Zinoviev. Pfaffian and the Kac--Ward Formula in the Two-Dimensional Ising Model. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Nonlinear dynamics, Tome 251 (2005), pp. 139-153. http://geodesic.mathdoc.fr/item/TM_2005_251_a5/