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

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

2006-07-25

arxiv.org/abs/cond-mat/0607647v1

Physical Review E 74, 020104(R) (2006).

Physics

Condensed Matter

Statistical Mechanics

4 Pages to appear in the Physical Review E (2006)

Scientific paper

10.1103/PhysRevE.74.020104

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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