2008/12/15 by Jerome Dubail, Jérôme Dubail, Jesper Lykke Jacobsen +1 · 40 citations
Mathematics · Physics and Astronomy · #Algebraic number #Annulus (botany) #Boundary value problem #Conformal field theory #Conformal map #Invariant (physics) #Ising model #Mathematical analysis #Mathematical physics #Mathematics #Partition function (quantum field theory) #Physics #Potts model #Quantum mechanics #Random Matrices and Applications #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP
paper · pdf · doi:10.1016/j.nuclphysb.2008.12.023
published in Nuclear Physics B 813(3), 430-459 (Elsevier BV) · 34 pages, 10 figures
arxiv created 2008/12/15 · openalex publication_date 2009/01/02 · arxiv updated 2017/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the two-boundary extension of a loop model - corresponding to the dense phase of the O(n) model, or to the Q=n2 state Potts model - in the critical regime -2 < n < 2. This model is defined on an annulus of aspect ratio τ. Loops touching the left, right, or both rims of the annulus are distinguished by arbitrary (real) weights which moreover depend on whether they wrap the periodic direction. Any value of these weights corresponds to a conformally invariant boundary condition. We obtain the exact seven-parameter partition function in the continuum limit, as a function of τ, by a combination of algebraic and field theoretical arguments. As a specific application we derive some new crossing formulae for percolation clusters.