We examine the large-N limit of quantum field models in the context of stochastic reduction of degrees of freedom. We then solve some simple two-dimensional models under the assumption that, in the above limit, the polynomial invariants are independent of the noise and the reduction variables. Then, we discuss the stability from the stochastic point of view and find explicit results for O(N) and ${\mathrm{CP}}^{\mathrm{N}\mathrm{-}1}$ models.

• Received 13 October 1987

DOI:https://doi.org/10.1103/PhysRevD.37.2225