Geodesic
Simple solution of two-dimensional ising model on a~torus in terms of Grassmann integrals
Teoretičeskaâ i matematičeskaâ fizika, Tome 64 (1985) no. 1, pp. 150-162

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A simple method is proposed for exact solution of the two-dimensional Ising model on a torus (lattice of finite size with periodic boundary conditions). The problem is solved through construction of a Grassmann representation for the partition function. The mirror Grassmann factorization for the Boltzmann weights and a special identity for Grassmaan functions are used. The method is mathematically completely rigorous. 
@article{TMF_1985_64_1_a12,
     author = {V. N. Plechko},
     title = {Simple solution of two-dimensional ising model on a~torus in terms of {Grassmann} integrals},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {150--162},
     publisher = {mathdoc},
     volume = {64},
     number = {1},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_64_1_a12/}
}
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V. N. Plechko. Simple solution of two-dimensional ising model on a~torus in terms of Grassmann integrals. Teoretičeskaâ i matematičeskaâ fizika, Tome 64 (1985) no. 1, pp. 150-162. http://geodesic.mathdoc.fr/item/TMF_1985_64_1_a12/