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 $k$ of the springs. We obtain the reduced localization lengths ${\Lambda }_M$ from calculated Lyapunov exponents for different system widths to roughly locate the squared critical transition frequency ${\omega }_{\text{c}}^2$. The data is finite-size scaled to acquire the squared critical transition frequency of ${\omega }_{\text{c}}^2=12.54\pm 0.03$ and a critical exponent of $\nu =1.55\pm 0.002$.

6 pages, 3 figures, 1 table, conference proceedings

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Cited by in corpus (3)

• Multifractal finite-size-scaling and universality at the Anderson transition
• Phonon localization in binary alloys with diagonal and off-diagonal disorder: A cluster Green's function approach
• Localization-delocalization transition for disordered cubic harmonic lattices