Static replica approach to critical correlations in glassy systems

Franz, Silvio; Jacquin, Hugo; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, Francesco
March 2013
Journal of Chemical Physics;Mar2013, Vol. 138 Issue 12, p12A540
Academic Journal
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 these critical fluctuations. By using this at the Gaussian level we obtain many physical quantities: the correlation length, the exponent parameter that controls the mode-coupling dynamical exponents for the two-point correlation functions, and the prefactor of the critical part of the four point correlation functions. Moreover, we perform a one-loop computation in order to identify the region in which 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.


Related Articles

  • Geometrical frustration and static correlations in hard-sphere glass formers. Charbonneau, Benoit; Charbonneau, Patrick; Tarjus, Gilles // Journal of Chemical Physics;Mar2013, Vol. 138 Issue 12, p12A515 

    We analytically and numerically characterize the structure of hard-sphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated with increasing fluid packing fraction, but to become increasingly...

  • Self-consistent Ornstein–Zernike approximation for the Yukawa fluid with improved direct correlation function. Reiner, A.; Ho\ye, J. S. // Journal of Chemical Physics;3/21/2008, Vol. 128 Issue 11, p114507 

    Thermodynamic consistency of the mean spherical approximation as well as the self-consistent Ornstein–Zernike approximation (SCOZA) with the virial route to thermodynamics is analyzed in terms of renormalized γ-ordering. For continuum fluids, this suggests the addition of a...

  • Systematic expansion in the order parameter for replica theory of the dynamical glass transition. Jacquin, Hugo; Zamponi, Francesco // Journal of Chemical Physics;Mar2013, Vol. 138 Issue 12, p12A542 

    It has been shown recently that predictions from mode-coupling theory for the glass transition of hard-spheres become increasingly bad when dimensionality increases, whereas replica theory predicts a correct scaling. Nevertheless if one focuses on the regime around the dynamical transition in...

  • Hardness and incipient plasticity in silicate glasses: Origin of the mixed modifier effect. Kjeldsen, Jonas; Smedskjaer, Morten M.; Mauro, John C.; Yuanzheng Yue // Applied Physics Letters;2/3/2014, Vol. 104 Issue 5, p051913-1 

    The scaling of Vickers hardness (Hv) in oxide glasses with varying network modifier/modifier ratio is manifested as either a positive or negative deviation from linearity with a maximum deviation at the ratio of about 1:1. In an earlier study [J. Kjeldsen et al., J. Non-Cryst. Solids 369, 61...

  • The shapes of cooperatively rearranging regions in glass-forming liquids. Stevenson, Jacob D.; Schmalian, Jörg; Wolynes, Peter G. // Nature Physics;Apr2006, Vol. 2 Issue 4, p268 

    The cooperative rearrangement of groups of many molecules has long been thought to underlie the dramatic slowing of liquid dynamics on cooling towards the glassy state. For instance, there exists experimental evidence for cooperatively rearranging regions (CRRs) on the nanometre length scale...

  • Critical-like behaviour of glass-forming liquids. Tanaka, Hajime; Kawasaki, Takeshi; Shintani, Hiroshi; Watanabe, Keiji // Nature Materials;Apr2010, Vol. 9 Issue 4, p324 

    Recently it has been revealed that when approaching the glass-transition temperature, Tg, the dynamics of a liquid not only drastically slows down, but also becomes progressively more heterogeneous. From our simulations and experiments of six different glass-forming liquids, we find that the...

  • Static triplet correlations in glass-forming liquids: A molecular dynamics study. Coslovich, Daniele // Journal of Chemical Physics;Mar2013, Vol. 138 Issue 12, p12A539 

    We present a numerical evaluation of the three-point static correlations functions of the Kob-Andersen Lennard-Jones binary mixture and of its purely repulsive, Weeks-Chandler-Andersen variant. In the glassy regime, the two models possess a similar pair structure, yet their dynamics differ...

  • On the Generalization of the Hébraud-Lequeux Model to Multidimensional Flows. Olivier, Julien; Renardy, Michael // Archive for Rational Mechanics & Analysis;May2013, Vol. 208 Issue 2, p569 

    In this article we build a model for multidimensional flows in soft glassy materials. The construction of the model is based on the ideas of Hébraud and Lequeux, but care is taken to build a frame-indifferent multidimensional model. The main goal of this article is to prove that the...

  • Freezing of Lennard-Jones-type fluids. Khrapak, Sergey A.; Chaudhuri, Manis; Morfill, Gregor E. // Journal of Chemical Physics;2/7/2011, Vol. 134 Issue 5, p054120 

    We put forward an approximate method to locate the fluid-solid (freezing) phase transition in systems of classical particles interacting via a wide range of Lennard-Jones-type potentials. This method is based on the constancy of the properly normalized second derivative of the interaction...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics