  We study the operator product expansion (OPE) of the auxiliary scalar field
\lambda(x) with itself, in the conformally invariant O(N) Vector Model for
2<d<4, to leading order in 1/N in a strip-like geometry with one finite
dimension of length L. We show that consistency of the finite-geometry OPE with
bulk OPE calculations requires the physical conditions of, either finite-size
scaling at criticality, or finite-temperature phase transition.
