Free Fermions and Two-Dimensional Ising Model
Abstract
The two-dimensional Ising model is representable as a lattice free-fermion field theory in terms of the integral over anticommuting Grassmann variables. The exact solution in a zero magnetic field then follows by evaluating Gaussian fermionic integral for partition function. It is argued that by switching on of a non-zero magnetic field the non-local and non-Gaussian fermionic terms appear in the action, which rather imply approximating methods of the analysis.
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