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The Erwin Schroedinger Institute for Mathematical Physics

Elliott Lieb (Princeton University): A Pfaffian formula for monomer-dimer partition functions

The monomer-dimer covering problem shows up in several areas of
physics and other fields.  While the partition function of the  pure dimer
covering problem on planar lattices was solved ages ago by Kasteleyn and
Fisher-Temperley in terms of Paffians (whose squares are easily computable
determinants), the inclusion of monomers (i.e., vertices uncovered by
dimers)  is an intractable problem.  Together with Alessandro Giuliani
and Ian Jauslin we have succeeded in utilizing an ancient theorem*
to write the partition function of a restricted monomer-dimer problem
as a Pfaffian. This is the model in which monomers are allowed on the
boundary vertices of an arbitrary planar graph. Flyer (pdf)

At a glance

Type: Lecture
When: Mar 15, 2016
from 03:00 PM to 04:00 PM
Where: ESI, Boltzmann Lecture Hall
Organizers: Jakob Yngvason (U Vienna)
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