Speaker: Dominic Else (PI)
Title: In search of diabolical critical points
Abstract: A phase transition is an example of a “topological defect” in the parameter space (not space-time!) of a quantum many-body system, statistical mechanical system, or field theory. In this talk, I will consider topological defects in parameter space of higher codimension. These have the property that equilibrium states undergo some kind of non-trivial winding as one moves around the defect in parameter space. I show that such topological defects exist even in classical statistical mechanical systems in the presence of spontaneous symmetry breaking, and describe their general structure in this context. I then introduce the term “diabolical critical point” (DCP), which is a higher-codimension analog of a continuous phase transition. I formulate a conjecture on the way that the topological invariant of the surrounding family gets imprinted on the DCP.