Angelini Maria Chiara, Biroli Giulio
Dipartimento di Fisica, Ed. Marconi, "Sapienza" Università di Roma, 00185 Roma, Italy;
Institut Physique Théorique Commissariat à l'Énergie Atomique Saclay, CNRS Unité d'Immunorégulation 2306, 91191 Gif Sur Yvette, France.
Proc Natl Acad Sci U S A. 2017 Mar 28;114(13):3328-3333. doi: 10.1073/pnas.1613126114. Epub 2017 Feb 21.
We develop a real space renormalization group analysis of disordered models of glasses, in particular of the spin models at the origin of the random first-order transition theory. We find three fixed points, respectively, associated with the liquid state, with the critical behavior, and with the glass state. The latter two are zero-temperature ones; this provides a natural explanation of the growth of effective activation energy scale and the concomitant huge increase of relaxation time approaching the glass transition. The lower critical dimension depends on the nature of the interacting degrees of freedom and is higher than three for all models. This does not prevent 3D systems from being glassy. Indeed, we find that their renormalization group flow is affected by the fixed points existing in higher dimension and in consequence is nontrivial. Within our theoretical framework, the glass transition results in an avoided phase transition.
我们对玻璃的无序模型，特别是随机一级相变理论起源的自旋模型，开展了实空间重整化群分析。我们分别找到了三个不动点，它们分别与液态、临界行为以及玻璃态相关。后两个是零温不动点；这为有效激活能尺度的增长以及接近玻璃化转变时弛豫时间随之大幅增加提供了一个自然的解释。下临界维度取决于相互作用自由度的性质，并且对于所有模型都高于三维。这并不妨碍三维系统成为玻璃态。实际上，我们发现它们的重整化群流受到高维中存在的不动点的影响，因此是非平凡的。在我们的理论框架内，玻璃化转变导致了一个避免的相变。
