Cluster Dynamic Mean Field Theory of Glass Transition

Recently, the infinite dimensional theory of the dynamics of super-cooled liquids was established in [1,2,3], and showed to be related to the mode coupling transition (MCT) theory [4]. One of the main mean field predictions is the existence of a sharp dynamical transition, akin to the MCT transition, at a temperature T_d, i.e. as the temperature approaches T_d from above, the relaxation time diverges. However, in three dimensional glass-formers this transition is smeared out and a smooth crossover takes place. We extend the infinite dimensional analysis by developing a cluster dynamic mean field theory (CDMFT) where clusters of particles interact in a mean field way, while correlations involving several particles are taken into account inside clusters. This allows us to progressively take into account correlations between particles and activated dynamical processes. In this talk we will present CDMFT and present results for three dimensional super-cooled liquids.

[1] Maimbourg.et.al Phys. Rev. Lett. 116 , 015902 (2016)
[2] G. Szamel Phys. Rev. Lett. 119, 15502 (2017)
[3] Agoritsas et al, J. Phys. A: Math. Theor. 52 144002 (2019)
[4] W. Götze, Complex dynamics of glass-forming liquids: A mode-coupling theory