The O(n) model on the annulus

Details The O(n) model on the annulus The O(n) model on the annulus

2006-04-19

arxiv.org/abs/math-ph/0604043v2

Physics

Mathematical Physics

20 pp. v.2: important references added to earlier work, minor typos corrected

Scientific paper

10.1007/s10955-006-9186-8

We use Coulomb gas methods to propose 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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