Lee-Yang theory and normal fluctuations

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Abstract
The convergence of the distribution of block spin variables to a product of independent normal Gaussians is rigorously proved for every ferromagnetic system with nonzero magnetic field. This result extends to more general situations and in fact a simple and general link is exhibited between the absence of a phase transition in the framework of Lee-Yang theory and the convergence to a normal Gaussian fixed point under the action of the renormalization group.