A test of conformal invariance: correlation functions on a disc

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Abstract
Using conformal invariance one can derive the correlation functions on a disc from those in the half-plane. The correlation function in the half-plane is determined by the 'small' conformal invariance up to an unknown function of one variable. By measuring, using the Monte Carlo method, the correlation function for two different configurations, the unknown function can be eliminated and one obtains a test of conformal invariance. It is shown that the Ising and the three-state Potts model pass the test for very small lattices.