Study of the localization-delocalization transition for phonons via transfer matrix method techniques

Abstract

We use a transfer-matrix method to study the localization properties of vibrations in a 'mass and spring' model with simple cubic lattice structure. Disorder is applied as a box-distribution to the force-constants κ of the springs. We obtain the reduced localization lengths ΛM from calculated Lyapunov exponents for different system widths to roughly locate the squared critical transition frequency ω2c The data is finite-size scaled to acquire the squared critical transition frequency of ω2c 12.5 ± 4 0.03 and a critical exponent of ν 1.55 ± 0.002. © Published under licence by IOP Publishing Ltd 2011.