Condensed Matter and Statistical Physics Journal Club
|Date:|| October 1, 2007
|| Kastelyn's exact solution to the dimer problem on a 2D planar
lattice and its recent application to Kagome
|| Samarth Chandra
|| The dimer problem on a lattice is the question of evaluating the
free energy of closed packings of dimers on lattices. Kastelyn and, independently, Temperley and Fisher in 1961 gave a procedure to reduce the problem to the
evaluation of a determinant, in the case of 2D planar lattices. On the
other hand the Kagome lattice has acquired considerable importance in condensed matter physics in recent times and an exact solution of the dimer problem on a
Kagome lattice is of interest.
There are two parts of this talk. First we review Kastelyn's procedure
for solving the dimer problem on any 2D planar lattice. In the second part,
we will discuss the recent closed form solution for the case of Kagome lattice by Wang and
Wu [Phys.Rev.E (Rapid Comm.), arXiv:cond-mat] . The final result is strikingly
simple - f(x,y,z) = (1/3) ln(4xyz).