Remarks about an "exact" RG theory of Goldstone modes

A renormalization group (RG) theory of Goldstone mode singularities in the O(n>1)-symmetric phi^4 model is discussed. This perturbative RG theory is claimed to be asymptotically exact, as regards the long-wave limit of the correlation functions, where it predicts a purely Gaussian behavior of the transverse correlation function. However, we show that the results of this theory are incorrect, and the Gaussian behavior originates from a rough error in mathematics. Other relevant perturbative theories are discussed, as well.