John Cardy - All Souls College, University of Oxford
Wednesday, August 23rd, 10:45AM EDT (Zoom meeting starts at 10:30 EDT)
Dimensional reduction in the random field Ising model revisited
Many years ago, it was suggested that the critical behavior of the random field Ising model in D dimensions should be the same as that of the pure model in D-2 dimensions, a result explained by Parisi and Sourlas in terms of an emergent supersymmetry. However, this appears to contradict a rigorous result that the random field model orders in D=3. I propose a resolution of this puzzle by inverting the question and asking what random model in d+2 dimensions corresponds to the pure model in d dimensions. In this talk I will provide an answer, using rigorous arguments based on cluster expansion ideas of Brydges and Imbrie, which avoid the use of field theory and replicas.