Radial marginal perturbation of two-dimensional systems and conformal invariance

Abstract

The conformal mapping w=(L/2π)\ln z transforms the critical plane with a radial perturbation αρ^{-y} into a cylinder with width L and a constant deviation α(2π/L)^y from the bulk critical point when the decay exponent y is such that the perturbation is marginal. From the known behavior of the homogeneous off-critical system on the cylinder, one may deduce the correlation functions and defect exponents on the perturbed plane. The results are supported by an exact solution for the Gaussian model.

Old paper, for archiving. 3 pages, RevTeX