Off-critical local height probabilities on a plane and critical partition functions on a cylinder

摘要

We compute off-critical local height probabilities in regime-III restricted solid-on-solid models in a 4N-quadrant spiral geometry, with periodic boundary conditions in the angular direction, and fixed boundary conditions in the radial direction, as a function of N, the winding number of the spiral, and tau, the departure from criticality of the model, and observe that the result depends only on the product N tau. In the limit N - 1, tau - tau(0), such that tau(0) is finite, we recover the off-critical local height probability on a plane, tau(0)-away from criticality. In the limit N - infinity, tau - 0, such that N tau = tau(0) is finite, and following a conformal transformation, we obtain a critical partition function on a cylinder of aspect-ratio tau(0). We conclude that the off-critical local height probability on a plane, tau(0)-away from criticality, is equal to a critical partition function on a cylinder of aspect-ratio tau(0), in agreement with a result of Saleur and Bauer. (C) 2018 The Author(s). Published by Elsevier B.V.