Critical behavior of n-vector model with quenched randomness

Abstract

We consider the Ginzburg-Landau phase transition model with O(n) symmetry (i.e., the n-vector model) which includes a quenched randomness, i.e., a random temperature disorder. We have proven rigorously that within the diagrammatic perturbation theory the quenched randomness does not change the critical exponents at n tending to 0, which is in contrast to the conventional point of view based on the perturbative renormalization group theory.