Leonard Huxley Lecture Theatre

Dr David Ridout
Department of Theoretical Physics

Phase transitions and critical phenomena have historically provided a number of challenges for theoretical and mathematical physicists.  At issue is the fact that the correlation length diverges in such systems, so it is difficult to model them with a small number of degrees of freedom.  A way to overcome this was found via Wilson's renormalization group wherein the scaling limit of critical systems could be argued to be equivalent to certain Euclidean quantum field theories.  In particular, conformal field theoretic methods then yield exact computations, in many cases, for universal quantities such as critical exponents and correlation functions.

Whilst undeniably successful, there is something vaguely discomforting about this program.  The physical models that are "solved" in the above manner are inherently probabilistic (eg. the Ising model), so it should be surprising, and perhaps alarming, that their analysis requires quantum field theory.  In the last ten years, mathematicians, inspired and disturbed by this, have wrought their own set of breakthroughs in studying these models.  Their approach is based upon probability, stochastic PDEs and conformal analysis.  It goes by the name "Schramm-Loewner Evolution" (SLE) and has, so far, been rewarded with two Fields medals.

 This talk aims to give a brief (and gentle) introduction to the ideas described above and how one could hope to reconcile the physicist's and mathematician's approaches to critical phenomena.

 Dr David Ridout is an Australian Research Fellow in the Department of Theoretical Physics and the Mathematical Sciences Institute.  He obtained his doctorate at the University of Adelaide in 2005, studying conformal field theory and applications to string theory.  He then held a postdoctoral fellowship from NSERC in Quebec (2005-2007), a Marie-Curie fellowship at DESY, Hamburg (2007-2009), and a fellowship from the CRM in Montreal (2010).  Since returning to Australia late last year, he has been exploring mathematical aspects of logarithmic conformal field theories, integrable sigma models and statistical lattice models.