Eur. Phys. J. E (2011) 34: 102
https://doi.org/10.1140/epje/i2011-11102-0

Regular Article

Field theory of fluctuations in glasses

¹ Laboratoire de Physique Théorique et Modèles Statistiques, CNRS et Université Paris-Sud 11, Bât. 100, 91405, Orsay Cedex, France
² Dipartimento di Fisica, INFN - Sezione di Roma I, IPFC-CNR, UOS Roma Sapienza Università di Roma, P.le Aldo Moro 2, I-00185, Roma, Italy

^* e-mail: silvio.franz@lptms.u-psud.fr

Received: 31 May 2011
Accepted: 1 August 2011
Published online: 26 September 2011

Abstract

We develop a field-theoretical description of dynamical heterogeneities and fluctuations in supercooled liquids close to the (avoided) MCT singularity. Using quasi-equilibrium arguments, we eliminate time from the description and we completely characterize fluctuations in the beta regime. We identify different sources of fluctuations and show that the most relevant ones are associated to variations of “self-induced disorder” in the initial condition of the dynamics. It follows that heterogeneites can be described through a cubic field theory with an effective random field term. The phenomenon of perturbative dimensional reduction ensues, well known in random field problems, which implies an upper critical dimension of the theory equal to 8. We apply our theory to finite size scaling for mean-field systems and we test its prediction against numerical simulations.