We review some aspects of the fermionic interpretation of the two-dimensionalIsing model. The use is made of the notion of the integral over theanticommuting Grassmann variables. For simple and more complicated 2D Isinglattices, the partition function can be expressed as a fermionic Gaussianintegral. Equivalently, the 2D Ising model can be reformulated as afree-fermion theory on a lattice. For regular lattices, the analytic solutionthen readily follows by passing to the momentum space for fermions. We alsocomment on the effective field-theoretical (continuum-limit) fermionicformulations for the 2D Ising models near the critical point.
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