Grassmann Variables and Exact Solutions for Two-Dimensional Dimer Models

1997/11/17 by R. Hayn, V. N. Plechko
Physics and Astronomy · #cond-mat.stat-mech #hep-lat #hep-th

paper · pdf

published as Yad. Fiz. 61 (1998) 2080-2084 [Phys.At.Nucl. 61 (1998) 1972-1977] · LaTeX, 1 + 10 pages, no figures. A talk given at the VIII International Conference on Symmetry Methods in Physics, JINR, Dubna, Russia, July 28 - August 2, 1997, to appear in the proceedings

arxiv created 1997/11/17 · arxiv updated 2009/11/30

Abstract

We discuss some aspects of a new noncombinatorial fermionic approach to the two-dimensional dimer problem in statistical mechanics based on the integration over anticommuting Grassmann variables and factorization ideas for dimer density matrix. The dimer partition function can be expressed as a Gaussian fermionic integral. For regular lattices, the analytic solution then follows by passing to the momentum space for fermions.

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