Disorder Effects in Dynamical Restoration of Spontaneously Broken Continuous Symmetry

We discuss the Euclidean quantum $O(N)$ model with $N=2$ in a continuous broken symmetry phase. We study the system at low temperatures in the presence of quenched disorder linearly coupled to the scalar field. Performing an average over the ensemble of all realizations of the disorder, we represent the average free energy in terms of a series of the moments of the partition function. In the one-loop approximation, we prove that there is a denumerable collection of moments that lead the system to develop critical behavior. Our results indicate that in an equilibrium system, the strongly correlation of the disorder in imaginary produces generic scale invariance in the massive modes.