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We consider the pair correlation functions of both the order parameter fieldand its square for phase ordering in the $O(n)$ model with nonconserved orderparameter, in spatial dimension $2\le d\le 3$ and spin dimension $1\le n\le d$.We calculate, in the scaling limit, the exact short-distance singularities ofthese correlation functions and compare these predictions to numericalsimulations. Our results suggest that the scaling hypothesis does not hold forthe $d=2$ $O(2)$ model. Figures (23) are available on request - emailbray@v2.ph.man.ac.ukComment: 23 pages, Plain LaTeX, M/C.TH.93/2

Phase-ordering dynamics of the O(n) model: Exact predictions and numerical results