Han Peters: Phase transitions and bifurcations (joint with Math. Colloquium)

Loosely speaking, a phase transition occurs when a small change in physical parameters leads to drastic changes of the physical observables. Quite similarly, a bifurcation occurs when a small change of the parameters leads to wildly different behavior of a dynamical system. Clearly there is a strong similarity.

In joint ongoing work with Misha Hlushchanka, we study the behavior of the independence polynomial (the partition function of the hard-core model in statistical physics) on recursively defined sequences of graphs. In this setting there is a clear correspondence between the recursion on the level of graphs, and the iteration of a rational map. By exploiting the dynamical behavior of these maps, the existence or absence of phase transitions can be proved.