Laboratoire de Physique Théorique et Modèles Statistiques, Centre National de la Recherche Scientifique et Université Paris-Sud 11, Unité Mixte de Recherche 8626, 91405 Orsay Cedex, France.
Proc Natl Acad Sci U S A. 2012 Nov 13;109(46):18725-30. doi: 10.1073/pnas.1216578109. Epub 2012 Oct 29.
We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature, we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we analytically study the critical behavior of a set of four-points correlation functions, from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the hypernetted chain approximation for the Gibbs free energy, and we find results that are consistent with numerical simulations.
我们开发了一种全微观复制场理论，用于研究玻璃动力学转变。通过研究动力学温度下出现的软模，我们得到了一个临界涨落的有效理论。这一分析得到了几个结果：我们给出了平均场临界指数的表达式，并对一组四点相关函数的临界行为进行了分析，从中可以提取动力学相关长度。最后，我们可以得到一个吉布斯判据，说明我们分析的有效性范围。我们在吉布斯自由能的超网链逼近下计算了所有这些量，发现与数值模拟结果一致。
