Free Fermions and Two-Dimensional Ising Model

2004/11/29 by V. N. Plechko
Physics and Astronomy · Mathematics · #math-ph #cond-mat.stat-mech #hep-lat #hep-th #math.MP #msc:82B20 #msc:82B10 #msc:82B26

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published as Proceedings of XXIII International Colloquium on Group Theoretical Methods in Physics, July 31--Aug 5, 2000, Dubna, Russia. Edited by A.N.Sissakian, G.S.Pogosyan and L.G.Mardoyan, Vol.2, (JINR Publ., Dubna, 2002), p.557--562 · LaTeX, 6 pages, no figures

arxiv created 2004/11/29 · arxiv updated 2009/12/01

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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