  Monte Carlo simulations of the 1D Ising model with ferromagnetic interactions
decaying with distance $r$ as $1/r^{1+\sigma}$ are performed by applying the
Swendsen-Wang cluster algorithm with cumulative probabilities. The critical
behavior in the non-classical critical regime corresponding to $0.5 <\sigma <
1$ is derived from the finite-size scaling analysis of the largest cluster.
