Theory of the quantized Hall effect (III) |
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Authors: | Herbert Levine Stephen B Libby Adrianus MM Pruisken |
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Institution: | Schlumberger-Doll Research, P.O. Box 307, Ridgefield, CT 06877, USA;Dept. of Physics, Brown University, Providence, RI 02912, USA;Schlumberger-Doll Research, PO Box 307, Ridgefield, CT 06877, USA |
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Abstract: | In the previous paper, we have demonstrated the need for a phase transition as a function of θ in the non-linear σ-model describing the quantized Hall effect. In this work, we present arguments for the occurrence of exactly such a transition. We make use of a dilute gas instanton approximation as well as present a more rigorous duality argument to show that the usual scaling of the conductivity to zero at large distances is altered whenever , n integer. This then completes our theory of the quantized Hall effect. |
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