Representation Theory and Mathematical Physics Seminar: Pfaffian Sign Theorem for the Dimer Model on a Triangular Lattice.

Seminar | November 16 | 2-3 p.m. | 732 Evans Hall

 Drazen Petrovic, Purdue University

 Department of Mathematics

We prove the Pfaffian Sign Theorem for the dimer model on a triangular lattice embedded in the torus. More specifically, we prove that the Pfaffian of the Kasteleyn periodic-periodic matrix is negative, while the Pfaffians of the Kasteleyn periodic-antiperiodic, antiperiodic-periodic, and antiperiodic-antiperiodic matrices are all positive. The proof is based on the Kasteleyn identities and on small weight expansions. As an application, we obtain an asymptotics of the dimer model partition function with an exponentially small error term. This is a joint work with Pavel Bleher and Brad Elwood.