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Radial marginal perturbation of two-dimensional systems and conformal invariance

L. Turban
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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.

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L. Turban. 2001-06-29. Radial marginal perturbation of two-dimensional systems and conformal invariance. https://doi.org/10.1103/physrevb.44.7051

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