Remembrances of Michael E. Fisher

Abstract

This contribution will be published in '50 years of the renormalization group', dedicated to the memory of Michael E. Fisher, edited by Amnon Aharony, Ora Entin-Wohlman, David Huse, and Leo Radzihovsky, World Scientific. These personal remembrances come in three parts. The first contains a brief personal perspective on Michael E. Fisher's contributions to science. The second tells how I came to work with Michael and describes events while I was under his supervision during my graduate years at Cornell University. The third part summarizes recent work, done in collaboration with Suraj Shankar, on thermalized buckling of isotopically compressed thin (perhaps atomically thin) sheets of materials such as graphene or MoS$_2$. These investigations were inspired by Michael's beautiful work on the effect of constraints at critical points, with fluctuations at all length scales, which leads to 'Fisher renormalization' of critical exponents. [1] Thin fluctuating sheets embedded in three dimensions, when they are tensionless as in a cantilever or 'diving board' geometry, are automatically at a critical point everywhere in a low temperature flat phase. However, when we consider thin sheets supported on multiple sides in various ways, Fisher's ideas lead to the inequivalence of isotensional and isometric thermodynamic ensembles, which triggers dramatic differences in some of the critical exponents associated with the two types of boundary conditions. [2] Readers not interested in my experiences while a student at Cornell University may only want to read parts I and III. There are also some concluding remarks.