Quantitative field theory of the glass transition

被引：42
|
作者：
Franz, Silvio [2 ,3 ]
Jacquin, Hugo [4 ,5 ]
Parisi, Giorgio [1 ,6 ]
Urbani, Pierfrancesco [2 ,3 ,6 ]
Zamponi, Francesco [7 ]
机构：
[1] Consiglio Nazl Ric Italy, Ist Nazl Fis Nucl Italy, Sez Roma 1, Ist Proc Chim Fis, I-00185 Rome, Italy
[2] Univ Paris 11, Unite Mixte Rech 8626, F-91405 Orsay, France
[3] CNRS, Lab Phys Theor & Modeles Stat, F-91405 Orsay, France
[4] Univ Paris 07, F-75205 Paris 13, France
[5] CNRS, Unite Mixte Rech 7057, Lab Matiere & Syst Complexes, F-75205 Paris 13, France
[6] Univ Roma La Sapienza, Dipartimento Fis, I-00185 Rome, Italy
[7] CNRS, Unite Mixte Rech 8549, Ecole Normale Super, Phys Theor Lab, F-75005 Paris, France
来源：
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | 2012年 / 109卷 / 46期
基金：
欧洲研究理事会;
关键词：
mode-coupling theory; perturbative expansion; replica theory; NONLINEAR SUSCEPTIBILITY; SUPERCOOLED LIQUIDS; DYNAMICS; REPLICA; LENGTH;
D O I：
10.1073/pnas.1216578109
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
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.
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页码：18725 / 18730
页数：6
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