2009/04/20 by Louis-Pierre Arguin, Louis‐Pierre Arguin, Yvan Saint-Aubin
Physics and Astronomy · Mathematics · #Theoretical and Computational Physics #Stochastic processes and statistical mechanics #Markov Chains and Monte Carlo Methods
paper · doi:10.1063/1.3116597
We study the Ising model on a half-infinite cylinder at the critical temperature. On the boundary circle, we fix four intervals of constant signs. Let θ1, θ2, θ3, and θ4 be the positions where the flips occur, labeled counterclockwise in that order. From each θ starts a contour between clusters of opposite signs. The contour leaving θ1 may end only at θ2 or θ4. Using an argument based on conformal field theory, we give the probability distribution that the contour leaving θ1 ends at θ2. The behavior of this function when θ2−θ1→0 is described by a power law with an exponent (53) that belongs to the Kac table but that corresponds to a nonunitarizable highest-weight representation. We check that this prediction agrees with a Monte Carlo simulation.