  The Ising model with ferromagnetic interactions that decay as $1/r^\alpha$ is
analyzed in the non-extensive regime $0\leq\alpha\leq d$, where the
thermodynamic limit is not defined. In order to study the asymptotic properties
of the model in the $N\rightarrow\infty$ limit ($N$ being the number of spins)
we propose a generalization of the Curie-Weiss model, for which the
$N\rightarrow\infty$ limit is well defined for all $\alpha\geq 0$. We
conjecture that mean field theory is {\it exact} in the last model for all
$0\leq\alpha\leq d$. This conjecture is supported by Monte Carlo heat bath
simulations in the $d=1$ case. Moreover, we confirm a recently conjectured
scaling (Tsallis\cite{Tsallis}) which allows for a unification of extensive
($\alpha>d$) and non-extensive ($0\leq\alpha\leq d$) regimes.
