CRITICAL-BEHAVIOR OF WEAKLY DISORDERED ANISOTROPIC SYSTEMS IN 2 DIMENSIONS

The critical behavior of two-dimensional (2D) anisotropic systems with weak quenched disorder described by the so-called generalized Ashkin- Teller model (GATM) is studied. In the critical region this model is s hown to be described by a multifermion field theory similar to the Gro ss-Neveu model with a few independent quartic coupling constants. Reno rmalization group calculations are used to obtain the temperature depe ndence near the critical point of some thermodynamic quantifies and th e large-distance behavior of the two-spin correlation function. The eq uation of state at criticality is also obtained in this framework. We find that random models described by the GATM belong to the same unive rsality class as that of the two-dimensional Ising model. The critical exponent nu of the correlation length for the three- and four-state r andom-bond Ports models is also calculated in a three-loop approximati on We show that this exponent is given by an apparently convergent ser ies in epsilon=c-1/2 (with c the central charge of the Ports model) an d that the numerical values of nu are very close to that of the 2D Isi ng model. This work therefore supports the conjecture (valid only appr oximately for the three- and four-slate Pelts: models) of a superunive rsality for the 2D disordered models with discrete symmetries.