Localization-delocalization transition for disordered cubic harmonic lattices

TL;DR

This paper investigates the phase transitions between localized and delocalized vibrational states in three-dimensional disordered harmonic lattices, revealing universal critical behavior similar to electronic Anderson localization.

Contribution

It demonstrates the universality of the localization-delocalization transition in cubic harmonic lattices with mass and spring disorder, confirming the critical exponent aligns with the Anderson model.

Findings

Critical exponent of localization length: ν ≈ 1.55

Universal transition behavior for mass and spring disorder

Consistent results from density of states and wave function analysis

Abstract

We study numerically the disorder-induced localization-delocalization phase transitions that occur for mass and spring constant disorder in a three-dimensional cubic lattice with harmonic couplings. We show that, while the phase diagrams exhibit regions of stable and unstable waves, the universality of the transitions is the same for mass and spring constant disorder throughout all the phase boundaries. The combined value for the critical exponent of the localization lengths of $\nu = 1.550^{+0.020}_{-0.017}$ confirms the agreement with the universality class of the standard electronic Anderson model of localization. We further support our investigation with studies of the density of states, the participation numbers and wave function statistics.