Grassmann Variables and Exact Solutions for Two-Dimensional Dimer Models

Physics – Condensed Matter – Statistical Mechanics

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LaTeX, 1 + 10 pages, no figures. A talk given at the VIII International Conference on Symmetry Methods in Physics, JINR, Dubna

Scientific paper

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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