Linking numbers for self-avoiding loops and percolation: application to the spin quantum hall transition |
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Authors: | Cardy |
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Institution: | Department of Physics-Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom and All Souls College, Oxford, United Kingdom. |
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Abstract: | Nonlocal twist operators are introduced for the O(n) and Q-state Potts models in two dimensions which count the numbers of self-avoiding loops (respectively, percolation clusters) surrounding a given point. Their scaling dimensions are computed exactly. This yields many results: for example, the number of percolation clusters which must be crossed to connect a given point to an infinitely distant boundary. Its mean behaves as (1/3sqrt3] pi) |ln( p(c)-p)| as p-->p(c)-. As an application we compute the exact value sqrt3]/2 for the conductivity at the spin Hall transition, as well as the shape dependence of the mean conductance in an arbitrary simply connected geometry with two extended edge contacts. |
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