講師 Tommaso Rizzo氏 (La Sapienza Univ, Rome)
題目 Mean-Field theory of Kinetically-Constrained-Models
日時 2023年1月19(木) 13:30- (サイバーメディアセンター豊中 6Fセミナールーム)
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https://us02web.zoom.us/meeting/register/tZ0uduqhpzMjGtSp6gjy8mYdO1JAM7gN2OFf
Abstract:
One of the most important questions regarding the nature of the glass transition is whether glassiness has a thermodynamic origin or it is a purely dynamics phenomenon, the so-called dynamic/structure dilemma. In this respect Kinetically-Constrained-Models represent an extreme case: they have trivial thermodynamic properties and yet, because of dynamic facilitation, display all the basic features of glassy dynamics, including two-step relaxation and dynamical heterogeneities.
After a general introduction of the topic I will present the mean-field theory of these models considering the Fredrickson-Andersen model on the Bethe lattice. Using certain properties of the dynamics observed in numerical experiments we have derived asymptotic dynamical equations equal to those of Mode-Coupling-Theory.
Analytical predictions obtained for the dynamical exponents are successfully compared with numerical simulations in a wide range of models including the case of generic values of the connectivity and the facilitation, random pinning and fluctuating facilitation. The theory is thus validated for both continuous and discontinuous transition and also in the case of higher order critical points characterized by logarithmic decays