The O(n) Model on the Annulus |
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Authors: | John Cardy |
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Institution: | (1) Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, UK;(2) All Souls College, Oxford, UK |
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Abstract: | We use Coulomb gas methods to derive an explicit form for the scaling limit of the partition function of the critical O(n) model on an annulus, with free boundary conditions, as a function of its modulus. This correctly takes into account the magnetic charge asymmetry and the decoupling of the null states. It agrees with an earlier conjecture based on Bethe ansatz and quantum group symmetry, and with all known results for special values of n. It gives new formulae for percolation (the probability that a cluster connects the two opposite boundaries) and for self-avoiding loops (the partition function for a single loop wrapping non-trivially around the annulus.) The limit n→0 also gives explicit examples of partition functions in logarithmic conformal field theory. |
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Keywords: | 2d critical behavior conformal field theory percolation self-avoiding walks |
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