The critical behaviour of the long-range Potts chain from the largest cluster probability distribution

We present the numerical study of the one-dimensional Potts model with power-law decaying ferromagnetic interactions. The largest cluster probability distribution is obtained by Monte Carlo simulations using the Swendsen–Wang cluster algorithm with cumulative probabilities. The finite-size scaling analysis of the largest cluster is used to derive the critical behaviour in the non-classical regime of this model for various values of q.