Mean-field expansion for spin models with medium-range interactions

We study the critical crossover between the Gaussian and the Wilson-Fisher fixed point for general O(N)-invariant spin models with medium-range interactions, We perform a systematic expansion around the mean-field solution, obtaining the universal crossover curves and their leading corrections, In particular 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. All rights reserved.