STAT_PHYS Seminar on 3 Feb 2012

[ivanisse]

SPECIAL SEMINAR IN STATISTICAL PHYSICS


Friday, 3 February 2012  -   11:30 a.m.

Luigi Stasi Seminar Room - Leonardo Bldg. - 1st floor


Francesco Caltagirone (University of Rome, Sapienza)

"On the exponents of the critical slowing down in Mode Coupling Theory"

Abstract:

An important prediction of Mode-Coupling-Theory (MCT) is the 
relationship between the decay exponents in the beta  regime: 
Gamma2(1-a)/Gamma(1-2a) = Gamma2(1+b)/Gamma(1+2b)= lambda.  In the 
original structural glass context this relationship follows from the MCT 
equations that are obtained making rather uncontrolled approximations. 
As a consequence, it is usually assumed that the relationship between 
the exponents is correct while lambda has to be treated like a tunable 
parameter. On the other hand, it is known that in some mean-field 
spin-glass models the dynamics is precisely described by MCT. When we 
are in the so called "schematic" case,  lambda can be computed exactly 
but, again, its computation becomes difficult when we consider more 
complex models including finite-dimensional ones. We have been able to 
unveil the physical meaning of lambda in complete generality, relating 
the dynamical parameter to the static Gibbs free energy and giving, 
thus, a ``recipe'' for its computation. In this new framework we compute 
the exponents a and b for some mean-field models and compare our results 
with numerical simulations or, when available, exact results obtained 
via purely dynamical equations.