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.

• Received 2 March 1978

DOI:https://doi.org/10.1103/PhysRevB.19.1515