Franz S, Spigler S
LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.
Phys Rev E. 2017 Feb;95(2-1):022139. doi: 10.1103/PhysRevE.95.022139. Epub 2017 Feb 28.
Disordered systems are characterized by the existence of many sample-dependent local-energy minima that cause a step-wise response when the system is perturbed. In this article we use an approach based on elementary probabilistic methods to compute the complete probability distribution of the jumps (static avalanches) in the response of mean-field systems described by replica symmetry breaking; we find a precise condition for having a power-law behavior in the distribution of avalanches caused by small perturbations, and we show that our predictions are in remarkable agreement both with previous results and with what is found in simulations of three-dimensional systems of soft spheres, either at jamming or at slightly higher densities.
无序系统的特征是存在许多依赖于样本的局部能量极小值，当系统受到扰动时，这些极小值会导致逐步响应。在本文中，我们使用一种基于基本概率方法的途径，来计算由副本对称性破缺描述的平均场系统响应中的跳跃（静态雪崩）的完整概率分布；我们找到了一个精确条件，用于确定由小扰动引起的雪崩分布中幂律行为的存在，并且我们表明，我们的预测与先前的结果以及在软球三维系统的模拟中所发现的结果（无论是在堵塞状态还是在略高的密度下）都非常吻合。
