Random elastic networks : 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 [Phys. Rev. Lett. 90, 148702 (2003)] and by Amir, Oreg and Imry [Phys. Rev. Lett. 105, 070601 (2010)] respectively. The principle is to eliminate iteratively the elementary oscillating mode of highest frequency associated with either a mass or a spring constant. To explain the accuracy of the strong disorder RG rules, we compare with the Aoki RG rules that are exact at fixed frequency.