The CPA solution of the anomalous Lyapunov exponent for disordered binary chains
Articles > Article · 2002
Authors: İbrahim AVGIN
EUROPEAN PHYSICAL JOURNAL B, Journal Indexed in SCI Expanded, International, 2002, vol 29, pp 437-440
DOI: 10.1140/epjb/e2002-00276-8
Summary
The Coherent Potential Approximation (CPA) self-consistent equation is calculated for a binary disordered chain introducing a simple transformation. The transformation reduces the CPA equation to a cubic polynomial whose complex roots are related to the Green function and their relation to the complex Lyapunov exponent is also established. This solution fruitfully captures essential aspects of the well-known anomalous scaling behaviors in a different and advantageous way. It is found that the anomalous behavior is strongly effected by the nature of these roots. A small disorder expansion is carried out for comparison with the previous weak disorder calculations. We found that the CPA reproduced the anomalous behavior of the exact calculations.