Radial marginal perturbation of two-dimensional systems and conformal invariance.

Abstract

The conformal mapping w=(L/2\ensuremath{\pi})lnz transforms the critical plane with a radial perturbation \ensuremath{\alpha}${\mathrm{\ensuremath{\rho}}}^{\mathrm{\ensuremath{-}}\mathit{y}}$ into a cylinder with width L and a constant deviation \ensuremath{\alpha}(2\ensuremath{\pi}/L${)}^{\mathit{y}}$ 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.