Scaling behavior of the localization length in random dimer harmonic chains with thermal correlations.

Abstract

The nature of the vibrational modes of a random dimer harmonic chain with thermal correlations is numerically investigated. It is obtained that the localization length ${\mathit{L}}_{\mathit{c}}$ does not scale with the annealing temperature T like the mean cluster size ${\ensuremath{\xi}}_{\mathit{a}}$ (ln${\ensuremath{\xi}}_{\mathit{a}}$\ensuremath{\propto}1/T). Instead, it obeys distinct scaling laws, namely ${\mathit{L}}_{\mathit{c}}$(\ensuremath{\omega},T)\ensuremath{\propto}${\mathit{T}}^{\mathrm{\ensuremath{-}}{\ensuremath{\nu}}_{\mathit{c}}}$${\mathit{L}}_{\mathit{c}}$(\ensuremath{\omega},\ensuremath{\infty}), with ${\ensuremath{\nu}}_{\mathit{c}}$=2.7 and ${\ensuremath{\nu}}_{\mathit{c}}$=3.9 both in the bottom and upper halves common band, respectively. \textcopyright{} 1996 The American Physical Society.