Random elastic networks: a strong disorder renormalization approach

Abstract

For arbitrary networks of random masses connected by random springs, we define a general strong disorder real-space renormalization (RG) approach that generalizes the procedures introduced previously by Hastings (2003 Phys. Rev. Lett. 90 148702) and by Amir et al (2010 Phys. Rev. Lett. 105 070601), respectively. The principle is to eliminate iteratively the elementary oscillating mode of highest frequency associated with either a mass or spring constant. To explain the accuracy of the strong disorder RG rules, we compare with the Aoki RG rules that are exact at a fixed frequency.