We study the critical crossover between the Gaussian and the Wilson-Fisher
fixed point for general O(N)-invariant spin models with medium-range intera
ctions, We perform a systematic expansion around the mean-field solution, o
btaining the universal crossover curves and their leading corrections, In p
articular we show that, in three dimensions, the leading correction scales
as R-3, R being the range of the interactions, We compare our results with
the existing numerical ones obtained by Monte Carlo simulations and present
a critical discussion of other approaches, (C) 1999 Elsevier Science B.V.
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