Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary

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Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary.

We consider the dimer-monomer problem for the rectangular lattice. By mapping the problem into one of close-packed dimers on an extended lattice, we rederive the Tzeng-Wu solution for a single monomer on the boundary by evaluating a Pfaffian. We also clarify the mathematical content of the Tzeng-Wu solution by identifying it as the product of the nonzero eigenvalues of the Kasteleyn matrix.

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ژورنال

عنوان ژورنال: Physical Review E

سال: 2006

ISSN: 1539-3755,1550-2376

DOI: 10.1103/physreve.74.020104