Integer quantum Hall transition: An S -matrix approach to random networks

In this paper we propose an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>S</a:mi></a:math>-matrix approach to numerical simulations of network models and apply it to random networks that we proposed in a previous work [I. A. Gruzberg, A. Klümper, W. Nuding, and A. Sedrakyan, ]. Random networks are modifications of the Chalker-Coddington (CC) model for the integer quantum Hall transition that more faithfully captures the physics of electrons moving in a strong magnetic field and a smooth disorder potential. This method has considerable advantages compared to the transfer matrix approach and gives the value <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>ν</b:mi><b:mo>≈</b:mo><b:mn>2.4</b:mn></b:mrow></b:math> for the critical exponent of the localization length in a random network. This finding confirms our previous result and is surprisingly close to the experimental value <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>ν</c:mi><c:mtext>expt</c:mtext></c:msub><c:mo>≈</c:mo><c:mn>2.38</c:mn></c:mrow></c:math> observed at the integer quantum Hall transition but substantially different from the CC value <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msub><d:mi>ν</d:mi><d:mtext>CC</d:mtext></d:msub><d:mo>≈</d:mo><d:mn>2.6</d:mn></d:mrow></d:math>.