LEE-YANG THEORY AND NORMAL FLUCTUATIONS

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. © 1979 The American Physical Society.