On dynamical correlations in supercooled liquids

We show how the growth of a dynamical correlation length and its associated susceptibility recently observed by the present authors and co-workers as T, is approached can be understood in an appropriate theoretical framework. We discuss some predictions for these quantities in the region below T, which have not yet been explored in numerical simulations. One of the most striking features of the physics of supercooled liquids and glasses is the high degree of universality underlying the glass transition, and the scaling laws characterizing the ‘avoided’ dynamical phase transition described by the modecoupling theory (Goetze 1989). Since the work of Kirkpatrick and Thirumalai (1987) and Kirkpatrick and Wolynes (1987a,b), we know that many of the fundamental features of glass physics are captured by a certain class of simple generalized spin-glass models. These are models described by a Hamiltonian H [ S ] which is a random Gaussian function of an extensive number of spin variables S == {S,}, i = 1,. . . , N , which can be real, Ising, Potts, etc., variables. Since the general features of these models are largely independent of the nature of the variables involved, it has become customary to consider spherical models, where the Si are real and subject to the constraint S’ = N such that the configuration space is an N the analytic treatment of the model, and we restrict our discussion here to this simplified model. The physics of this model depends on the range of the correlation furiction H [ S ] H [ S ’ ] , which is usually taken to be a function of the overlap q(S, S’) = (1/N) C j S,S,‘, that is dimensional sphere of radius N .% . This choice allows for important simplifications in The function f ( q ) is an increasing function of q; the more similar the two configurations, the more correlated the energies are. If the correlations decay rapidly enough (faster than q2), the physics of the model display many features in common with supercooled liquids and glasses (Mezard and Parisi 1990, Nieuwenhuizen 1995). The case f ( q ) = q p is known as p-spin model. The various aspects of glassy )I E-mailt [email protected]. Philosophical Magazine B ISSN 0141-8637 pnnt/ISSN 1463-6417 online