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 4 N -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 τ , the departure from criticality of the model, and observe that the result depends only on the product N τ . In the limit N → 1 , τ → τ 0 , such that τ 0 is finite, we recover the off-critical local height probability on a plane, τ 0 -away from criticality. In the limit N → ∞ , τ → 0 , such that N τ = τ 0 is finite, and following a conformal transformation, we obtain a critical partition function on a cylinder of aspect-ratio τ 0 . We conclude that the off-critical local height probability on a plane, τ 0 -away from criticality, is equal to a critical partition function on a cylinder of aspect-ratio τ 0 , in agreement with a result of Saleur and Bauer.