GRASSMANN VARIABLE ANALYSIS FOR DIMER PROBLEMS IN 2 DIMENSIONS

We present a new non-combinatorial interpretation for the fermionic na ture of the 2D dimer problem. The partition functions of the closed-pa cked dimer models settled on the most general inhomogeneous rectangula r, triangular, and hexagonal lattice nets are obtained as fermionic Ga ussian integrals. These Gaussian representations provide the analytic results for the partition functions and dimer-dimer correlations for a variety of regular lattices, and can also be applied to analyse defec ts, boundary influences, effects of disorder etc, in dimer models.