Geometrical aspects of critical Ising configurations in two dimensions

Abstract

We present a physical interpretation of a number of exotic exponents of the two-dimensional Ising model, i.e., exponents that do have a conformal classification, but outside the unitary grid. They describe the scaling behavior of geometric properties of Ising and random clusters. For instance, the probability that two spins at a distance r lie on the perimeter of the same Ising cluster decays as ${\mathit{r}}^{\mathrm{\ensuremath{-}}5/4}$ at criticality. These results are obtained via mappings on the Coulomb gas. A part of the Coulomb gas scenario is verified by means of finite-size scaling of transfer-matrix results.