STABILITY OF THE RENORMALIZATION-GROUP IN THE 2D RANDOM ISING AND BAXTER-MODELS WITH RESPECT TO REPLICA SYMMETRY-BREAKING

We study the critical properties of the weakly disordered two-dimensio nal Ising and Baxter models in terms of the renormalization group (RG) theory generalized to take into account replica symmetry breaking (RS B) effects. Recently it has been shown that the traditional replica-sy mmetric RG flows in the dimension D = 4-E are unstable with respect to the RSB potentials and a new spin-glass type critical phenomena has b een discovered (Dotsenko Vik S, Harris B, Sherrington D and Stinchbomb e R 1995 J. Phys. A: Math. Gen. 28 3093; Dotsenko Vik S and Feldman D E 1995 J. Phys. A: Math. Gen. 28 5183). In contrast, here it is demons trated that in the considered two-dimensional systems the renormalizat ion-group hows are stable with respect to the RSB modes. It is shown t hat the solution of the renormalization group equations with arbitrary starting RSB coupling matrix exhibits asymptotic approach to the trad itional replica-symmetric ones. Thus, to leading order the non-perturb ative RSB degrees of freedom do not affect the critical phenomena in t he two-dimensional weakly disordered Ising and Baxter models studied e arlier.