Restoration of a spontaneously broken symmetry in a Euclidean quantum λ φd+14 model with quenched disorder

We investigate the low-temperature behavior of a system in a spontaneously broken symmetry phase described by a Euclidean quantum λφd+14 model with quenched disorder. We study the effects of the disorder linearly coupled to the scalar field using a series representation for the averaged generating functional of connected correlation functions in terms of the moments of the partition function. To deal with the strongly correlated disorder in imaginary time, we employ the equivalence between the model defined in a d-dimensional space with imaginary time with the statistical field theory model defined on a space Rd×S1 with anisotropic quenched disorder. Next, using stochastic differential equations and fractional derivatives, we obtain the Fourier transform of the correlation functions of the disordered system at tree level. In one-loop approximation, we prove that there is a denumerable collection of moments of the partition function that can develop critical behavior. Our main result is that, even with the bulk in the ordered phase, there are many critical compactified lengths that take each of the moments of the partition function from an ordered to a disordered phase. This is a sign of generic scale invariance emergence in the system.