Critical behavior of the long-range Ising chain from the largest-cluster probability distribution

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.