Localization length index in a Chalker-Coddington model: a numerical study

Abstract

We calculated numerically the localization length index $\nu$ for the Chalker-Coddington model of the plateau-plateau transitions in the quantum Hall effect. By taking into account finite size effects we have obtained $\nu =2.593\pm 0.0297$. The calculations were carried out by two different programs that produced close results, each one within the error bars of the other. We also checked the possibility of logarithmic corrections to finite size effects and found, that they come with much larger error bars for $\nu$.

5 pages, 3 figures, 1 table

References in corpus (13)

• Scaling Theory of the Integer Quantum Hall Effect
• Critical exponent for the quantum Hall transition
• Scaling in Plateau-to-Plateau Transition: A Direct Connection of Quantum Hall Systems with Anderson Localization Model
• Multifractality at the quantum Hall transition: Beyond the parabolic paradigm
• Quantum Hall effect in a one-dimensional dynamical system
• Toward a theory of the integer quantum Hall transition: continuum limit of the Chalker-Coddington model
• Towards a theory of the integer quantum Hall transition: from the nonlinear sigma model to superspin chains
• Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition
• Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect
• Network Models of Quantum Percolation and Their Field-Theory Representations
• Evidence for the PSL(2$|$2) Wess-Zumino-Novikov-Witten model as a model for the plateau transition in Quantum Hall effect: Evaluation of numerical simulations
• On the theory of plateau-plateau transitions in Quantum Hall Effect
• Strong Coupling Fixed Points of Current Interactions and Disordered Fermions in 2D

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