Tues. seminar at SISSA

[Cond.Matt. & Stat.Mech.Section]

JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR

 

Tuesday, 20 November   -   11:00 a.m.

 



SISSA, Santorio Building,    Room 128 (1st Floor)

 

 

Francesco ZAMPONI     ( École Normale Supérieure, Paris )

 

 

"Ginzburg criterion for the glass transition"

 

 

Abstract

 

I will discuss the onset of slow relaxation in glassy systems by constructing a static replica field theory approach to the problem.  At the mean field level, criticality in the four point correlation functions arises because of the presence of soft modes and I will present an effective replica field theory for these critical fluctuations.  At the Gaussian level many physical quantities are obtained: the correlation length, the exponent parameter that controls the Mode-Coupling dynamical exponents for the two-point correlation functions, and the prefactor of the critical part of the four point correlation functions.  A one-loop computation allows to identify the region in which the mean field Gaussian approximation is valid.  The result is a Ginzburg criterion for the glass transition, which confirms that the upper critical dimension for the glass transition is d=8.  Finally, I will present numerical results for hard spheres in dimension d ranging from 3 to 9 that support the analytical results.