Spring 2012
Venue: HSB 317
The theme for the current semester is The Ising Model. We plan to study exact solutions to the 1d and 2d Ising model, Kasteleyn's exact solution to the dimer model(perfect matchings) and how the 2d Ising model is an example of a dimer model, Sorin Istrail's proof of the NP-completeness of the non-planar Ising model (e.g. the 3d Ising model).
The exact solution of the 2d Ising model — II
Speaker: B. Srivatsan
Time: 2 pm
Abstract: Last week, we saw that the partition function of the two-dimensional Ising model on a square-lattice with periodic boundary conditions and $mn$ sites can be written as the trace of the $m$-th power of a $2^n\times 2^n$ matrix. In order to compute the partition function in the thermodynamic limit i..e, when $m,n \rightarrow \infty$, we need to determine its largest eigenvalue. Thus, we need to find the eigenvalues of the matrix and then determine the largest eigenvalue.
Ref: Boris Kastening, Pedestrian solution of the two-dimensional Ising model, arXiv:cond-mat/0104398
