The O(n) model on the annulus

Abstract

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.

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

References in corpus (5)

• Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
• Linking numbers for self-avoiding walks and percolation: application to the spin quantum Hall transition
• Logarithmic torus amplitudes
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Cited by in corpus (20)

• Associative-algebraic approach to logarithmic conformal field theories
• Universal entanglement entropy in 2D conformal quantum critical points
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions
• Conformal boundary loop models
• Correction-to-scaling exponent for two-dimensional percolation
• Conformal boundary conditions in the critical O(n) model and dilute loop models
• Two-dimensional O(n) models and logarithmic CFTs
• Jamming and percolation properties of random sequential adsorption with relaxation
• Conformal partition functions of critical percolation from $D_3$ Thermodynamic Bethe Ansatz equations
• Breaking universality in random sequential adsorption on a square lattice with long-range correlated defects
• Fractal dimensions of the Q-state Potts model for the complete and external hulls
• SLE on doubly-connected domains and the winding of loop-erased random walks
• Zeros of the i.i.d. Gaussian Laurent series on an annulus: weighted Szegő kernels and permanental-determinantal point processes
• Werner's Measure on Self-Avoiding Loops and Welding
• The elastic and directed percolation backbone
• A generalisation of Schramm's formula for SLE(2)
• Correction-to-scaling exponent for percolation and the Fortuin--Kasteleyn Potts model in two dimensions
• Double Transition in a Model of Oscillating Percolation
• Boundary conformal field theories and loop models