Scaling concepts for the dynamics of viscous liquids near an ideal glassy state

Abstract

Motivated by recent mean-field theories of the structural glass transition and of the Potts glass model we formulate a scaling and droplet picture of an assumed ideal structural glass transition. The phase transition is a random first-order phase transition where the supercooled-liquid phase is composed of glassy clusters separated by interfaces or domain walls. Because of entropic driving forces the glassy clusters are continually being created and destroyed. As the ideal transition temperature is approached the entropic driving force vanishes and the size of the glassy clusters diverges with an exponent of \ensuremath{\nu}=2/d. All long-time dynamical processes are activated and the Vogel-Fulcher law is obtained for the liquid-state relaxation time.