Fermionic Integrals and Analytic Solutions for Two-Dimensional Ising Models

Details Fermionic Integrals and Analytic Solutions for Two-Dimensional Ising Models Fermionic Integrals and Analytic Solutions for Two-Dimensional Ising Models

1998-12-31

arxiv.org/abs/cond-mat/9812434v1

J. Phys. Studies, Vol.1, No.4 (1997) 554-563

Physics

Condensed Matter

Statistical Mechanics

LaTeX, 14 pages, no figures

Scientific paper

We review some aspects of the fermionic interpretation of the two-dimensional Ising model. The use is made of the notion of the integral over the anticommuting Grassmann variables. For simple and more complicated 2D Ising lattices, the partition function can be expressed as a fermionic Gaussian integral. Equivalently, the 2D Ising model can be reformulated as a free-fermion theory on a lattice. For regular lattices, the analytic solution then readily follows by passing to the momentum space for fermions. We also comment on the effective field-theoretical (continuum-limit) fermionic formulations for the 2D Ising models near the critical point.

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