Randomly dilute spin models: A six-loop field-theoretic study

We consider the Ginzburg-Landau MN model that describes M N-vector cubic models with O(M)-symmetric couplings. We compute the renormalization-group functions to six-loop order in d=3. We focus on the limit N->O which describes the critical behavior of an M-vector model in the presence of weak quenched disorder. We perform for the critical exponents: y=1.330(17), v=0.678(10), eta = 0.030(3), alpha = -0.034(30), Beta = 0.349(5), omega = 0.25(10). For M greater than or equal to 2 we show that the O(M) fixed point is stable, in agreement with general nonperturbative arguments, and that no random fixed point exists.