Critical behavior of disordered spin systems in two and three dimensions

Abstract

A field-theoretic treatment of Grinstein and Luther's model for describing critical phenomena in two- and three-dimensional dilute magnetic systems is presented. With the use of the loop expansion and a simple resummation technique, all the relevant features of the $\epsilon$-expansion treatment are confirmed. A crossover to random critical behavior is observed for a number of spin components $M<\mathrm{}{M}_c$, where $M_c\simeq 1.19$ in two dimensions and $M_c\simeq 2.01$ in three dimensions (3D). The first reliable evaluation of the critical exponents for the dilute 3D Ising model is also given.