Speaker: Anton Nazarov (St. Petersburg State University)
Title: Finite-size scaling of free energy in the dimer model on a
hexagonal domain
Abstract: In the talk we will consider dimer model on a hexagonal lattice. This
model can be seen as a ``pile of cubes in the corner''.
I will review Kasteleyn orientation and classical MacMahon formula for
the number of configurations. I will briefly discuss the connection with
the alternating sign matrices and 2d Ising model.
Than we will use MacMahon formula for the partition function to derive
the finite-size corrections to the scaling behavior of free energy in
the limit of lattice mesh tending to zero and temperature tending to
infinity.
We will discuss physical and mathematical meaning of the expansion
coefficients and compare theoretical results with Monte-Carlo
simulations. In particular, central charge of the effective field theory
is recovered from the coefficient of the logarithmic term.