Abstract | We present an application of the Grassmann algebra to the problem of the
monomer-dimer statistics on a two-dimensional square lattice. The exact
partition function, or total number of possible configurations, of a system of
dimers with a finite set of n monomers with fixed positions can be expressed
via a quadratic fermionic theory. We give an answer in terms of a product of
two pfaffians and the solution is closely related to the Kasteleyn result of
the pure dimer problem. Correlation functions are in agreement with previous
results, both for monomers on the boundary, where a simple exact expression is
available in the discrete and continuous case, and in the bulk where the
expression is evaluated numerically. |