Special Seminar in Statistical Physics: " On the exponents of the critical slowing down in Mode Coupling Theory "
Starts 3 Feb 2012 11:30
Ends 3 Feb 2012 20:00
Central European Time
ICTP
Leonardo da Vinci Building Luigi Stasi Seminar Room
Strada Costiera, 11
I - 34151 Trieste (Italy)
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.