8 January, 2010
Abstract
These lectures provide some introduction to the study of glasses based on the replica formalism.The replica approach presented here is a first principle's approach which aims at deriving the main glass properties from the microscopic Hamiltonian. In contrast to the old use of replicas in the theory ofdisordered systems, this replica approach applies also to systems without quenched disorder (in this sense, replicas have nothing to do with computing the average of a logarithm of the partition function). It has the advantage of describing in an unified setting both the behaviour near the dynamic transition (mode coupling transition) and the behaviour near the equilibrium `transition' (Kauzmann transition) that is present in fragile glasses.
The replica method may be used to solve simple mean field models, providing explicit examples of systems that may be studied analytically in great details and behave similarly to the experiments. Finally, using the replica formalism and some well adapted approximation schemes, it is possible to do explicit analytic computations of the properties of realistic models of glasses. The results of these first principle computations are in reasonable agreement with numerical simulations. The lecture will focus on the main concepts underlying the approach, and give a first introduction to some of the computations that can be done in this framework.
References and suggested reading
- M. Mezard and G. Parisi, http://arxiv.org/abs/0910.2838
- M. Mezard and G. Parisi, Thermodynamics of glasses: a first principle computation, Phys. Rev. Lett. 82 (1999) 747
- M. Mezard and G. Parisi, A first principle computation of the thermodynamics of glasses, J. Chem.Phys. 111, 1076 (1999)
- M. Mezard, First steps in Glass Theory, in "More is different", Ong and Bhatt editors, Princeton (2002)
- M. Mezard, Statistical Physics of the Glass Phase, proceedings of StatPhys XXI, Physica A 306 (2002) 25