We estimate, using a large-scale Monte Carlo simulation, the critical exponents of the antiferromagnetic Heisenberg model on a stacked triangular lattice. We obtain the following estimates: $γ/ν= 2.011 \pm .014 $, $ν= .585 \pm .009 $. These results contradict a perturbative
2+ε Renormalization Group calculation that points to Wilson-Fisher O(4) behaviour. While these results may be coherent with
4−ε results from Landau-Ginzburg analysis, they show the existence of an unexpectedly rich structure of the Renormalization Group flow as a function of the dimensionality and the number of components of the order parameter.
The equality φ = γ between the exponent φ, which describes crossover from zero to finite-random-field critical behaviour, and the order parameter susceptibility exponent, γ, is shown to be replaced by φ > γ when the random exchange dominates. Rough renormalization group estimates yield φ/γ ≃ 1.1 for three-dimensional random Ising models. The implications to experiments on dilute antiferromagnets in uniform fields are discussed. Similarly to spin glasses, the nonlinear susceptibility of the latter is shown to diverge as ( T - T N ) -0.7 .