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Center for Nonlinear Studies |
The understanding of critical phenomena has benefited greatly from the advent of field theoretic techniques, in particular the renormalization group. Almost 40 years after Leo Kadanoff's introduction of “block spins” and more than 30 years after Michael E. Fisher and Kenneth Wilson's seminal article on critical phenomena, the renormalization group is part of our textbook understanding of phase transitions and helped to form the very notion of universality. Field theoretic renormalisation group is no less successful in non-equilibrium. Yet, plenty of models remain elusive to this method, due not only to the absence of a small coupling, but also because of the sheer plethora of models and universality classes. Non-perturbative techniques might provide an alternative avenue, being able to handle strong coupling regimes and a very diverse range of models. In this talk I will briefly trace the history of the renormalization group and its different flavours. The non-perturbative renormalization group is then introduced, initially focusing on the exactly soluble free theory. Using model A as a touchstone, various central features are assessed, exposing fundamental differences to traditional techniques, as well as key questions and advantages. I would like to promote the non-perturbative renormalisation group as a new, exciting and very promising path to tackle some of the more recent and hitherto unsolved questions in non-equilibrium statistical mechanics.