Silvio Franz, Hugo Jacquin, Giorgio Parisi, Pierfrancesco Urbani, Francesco Zamponi
We discuss the slow relaxation phenomenon in glassy systems by means of replicas by constructing a static field theory approach to the problem. At the mean field level we study how criticality in the four point correlation functions arises because of the presence of soft modes and we derive an effective replica field theory for this critical fluctuations. By using this at the Gaussian level we obtain many physical quantities: the correlation length, the exponent parameter that controls both Mode-Coupling dynamical exponents for the correlation functions and also the prefactor of the critical part of the four point correlation functions. Moreover we perform a one-loop computation in order to see in which region the mean field Gaussian approximation is valid. The result is a Ginzburg Criterion for the glass transition. We define and compute in this way a proper Ginzburg number. Finally, we present numerical values of all these quantities obtained from the Hypernetted Chain approximation for the replicated liquid theory.
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http://arxiv.org/abs/1210.7304
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