Stability of the renormalization group in the 2D random Ising and Baxter models with respect to replica symmetry breaking
Abstract
We study the critical properties of the weakly disordered twodimensional Ising and Baxter models in terms of the renormalization group (RG) theory generalized to take into account replica symmetry breaking (RSB) effects. Recently it has been shown that the traditional replicasymmetric RG flows in the dimension 03054470/29/15/008/img1 are unstable with respect to the RSB potentials and a new spinglass type critical phenomena has been discovered (Dotsenko Vik S, Harris B, Sherrington D and Stinchbombe 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 demonstrated that in the considered twodimensional systems the renormalizationgroup flows are stable with respect to the RSB modes. It is shown that the solution of the renormalization group equations with arbitrary starting RSB coupling matrix exhibits asymptotic approach to the traditional replicasymmetric ones. Thus, to leading order the nonperturbative RSB degrees of freedom do not affect the critical phenomena in the twodimensional weakly disordered Ising and Baxter models studied earlier.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 August 1996
 DOI:
 10.1088/03054470/29/15/008
 arXiv:
 arXiv:condmat/9512158
 Bibcode:
 1996JPhA...29.4331F
 Keywords:

 Condensed Matter
 EPrint:
 8 pages, latex