Large-N reduction in spin systems and Griffiths singularities

We apply the quenched Eguchi-Kawai reduction procedure to N-component spin models. We first recover the equivalence of the O(N) symmetric Heisenberg model with the spherical model at large N, and we extend it to the case where a quenched random external field is present. When the random field has a gaussian distribution, we show that Griffiths singularities disappear as N → ∞.