WEAK QUENCHED DISORDER AND CRITICALITY: RESUMMATION OF ASYMPTOTIC(?) SERIES

Abstract

In this review paper, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of the available experimental and theoretical results as well as results of MC simulations of these phenomena. We concentrate on three cases: (i) uncorrelated random-site disorder, (ii) long-range correlated random-site disorder, and (iii) random anisotropy.Today, the standard analytical description of critical behavior is given by renormalization group results refined by resummation of the perturbation theory series. The convergence properties of the series are unknown for most disordered models. The main object of this review is to discuss the peculiarities of the application of resummation techniques to perturbation theory series of disordered models.