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Graduate Seminar

Chris Potter
Carnegie Melllon University
Title: THE RANDOM-CLUSTER MODEL OF VARIOUS PHYSICAL SYSTEMS

Abstract: In my last presentation in the spring, I discussed several algorithms for solving (or at least estimating statistical properties of solutions of) the Ising model and Potts models of the magnetic interaction of ferromagnetic crystals. Some of those algorithms made use of the fact that the Ising model can be recast as a percolation problem.

In this presentation, I will go through the main points of the 1971 paper of Fortuin and Kastelyn which provides the mathematical background for this fortuitous relationship. In fact, the "random-cluster model" defined in that paper has not only the Ising and percolation models as special cases, but also the graph coloring problem and the problem of deducing current on each segment of a linear electrical network.

Date: Tuesday, October 12, 2010
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Daniel Spector