A gadget for reducing the Ising model to matchings

01/24/2012 - 12:15pm
01/24/2012 - 1:10pm
Mark Huber (CMC)

In my talk last semester in the seminar, I presented a classic result: the problem of counting the number of solutions to a logic formula can be turned into a problem of summing weighted perfect matchings in a graph. The key idea was the use of a combinatorial "gadget". In this talk I'll present a gadget developed with my first graduate student, Jenny Law, that allows for what is called a simulation reduction. The reduction works as follows: if you are able to sample randomly from a weighted distribution on perfect matchings in a graph, then you can also simulate from the Ising model, a classical model from statistical physics that has been heavily studied since its inception in the 1920's. (http://arxiv.org/abs/0907.0477)

Millikan 134 (Pomona College)