Radial marginal perturbation of two-dimensional systems and conformal invariance

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The conformal mapping w=(L/2π) 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.