Free Fermions and Two-Dimensional Ising Model

Details Free Fermions and Two-Dimensional Ising Model Free Fermions and Two-Dimensional Ising Model

2004-11-29

arxiv.org/abs/math-ph/0411084v1

Proceedings of XXIII International Colloquium on Group Theoretical Methods in Physics, July 31--Aug 5, 2000, Dubna, Russia. Ed

Physics

Mathematical Physics

LaTeX, 6 pages, no figures

Scientific paper

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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