RADIAL MARGINAL PERTURBATION OF 2-DIMENSIONAL SYSTEMS AND CONFORMAL-INVARIANCE

The conformal mapping w = (L/2-pi)lnz transforms the critical plane with a radial perturbation alpha-rho-y into a cylinder with width L and a constant deviation alpha-(2-pi/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.