Universality and multifractal behaviour of spin-spin correlation functionsin disordered Potts models

We report a transfer matric study of the random bond q-state Potts model in the vicinity of the Ising model q = 2. We draw attention to a precise dete rmination of magnetic scaling dimensions in order to compare with perturbat ive results. Universality is checked by the computation of the spin-spin co rrelation function decay exponent obtained with different types of probabil ity distributions of the coupling strengths. Our numerical data, compared t o perturbative results for the second moment of the correlation function, o btained with both replica symmetry and replica symmetry breaking schemer, a re conclusively in favour of the replica symmetric calculations. The multif ractal behaviour of higher moments as well as that of typical correlation f unctions are also investigated and a comparison is made with the perturbati ve expansions. Finally, the shape of the correlation function probability d istribution is analyzed. (C) 2000 Elsevier Science B.V. All rights reserved .