Exact Lyapunov exponent of the harmonic magnon modes of one-dimensional Heisenberg-Mattis spin glasses

Reza Sepehrinia, M. D. Niry, B. Bozorg, M. Reza Rahimi Tabar, and Muhammad Sahimi
Phys. Rev. B 77, 104202 – Published 10 March 2008

Abstract

A mapping is developed between the linearized equation of motion for the dynamics of the transverse modes at T=0 of the Heisenberg-Mattis model of one-dimensional (1D) spin glasses and the (discretized) random wave equation. The mapping is used to derive an exact expression for the Lyapunov exponent (LE) of the magnon modes of spin glasses and to show that it follows anomalous scaling at low magnon frequencies. In addition, through numerical simulations, the differences between the LE and the density of states of the wave equation in a discrete 1D model of randomly disordered media (those with a finite correlation length) and that of continuous media (with a zero correlation length) are demonstrated and emphasized.

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  • Received 5 August 2007

DOI:https://doi.org/10.1103/PhysRevB.77.104202

©2008 American Physical Society

Authors & Affiliations

Reza Sepehrinia1, M. D. Niry1, B. Bozorg1, M. Reza Rahimi Tabar1,2, and Muhammad Sahimi3,*

  • 1Department of Physics, Sharif University of Technology, Tehran 11155-9161, Iran
  • 2Institute of Physics, Carl von Ossietzky University, D-26111 Oldenburg, Germany
  • 3Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA

  • *Corresponding author; moe@iran.usc.edu

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Vol. 77, Iss. 10 — 1 March 2008

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