Physica A 314 (2002) 448–453 www.elsevier.com/locate/physa The critical behaviour of the long-range Potts chain from the largest cluster probability distribution Katarina Uzelac a ; ∗ , Zvonko Glumac b a Institute of Physics, P.O.B. 304, Bijeni cka 46, HR-10000 Zagreb, Croatia b Faculty of Electrical Engineering, Kneza Trpimira 2B, 31 000 Osijek, Croatia Abstract We present the numerical study of the one-dimensional Potts model with power-law decay- ing ferromagnetic interactions. The largest cluster probability distribution is obtained by Monte Carlo simulations using the Swendsen–Wang cluster algorithm with cumulative probabilities. The nite-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. c  2002 Elsevier Science B.V. All rights reserved. PACS: 05.50.+q; 64.60.Cn Keywords: Phase transitions; q-state Potts model; Long-range interactions; Monte-Carlo simulations The models involving long-range interactions have an important role in describ- ing many complex systems, from physics to economy or biology, but the equilibrium critical phenomena in these models are still not well understood and deserve further attention. We consider here the 1d Potts model with long-range interactions dened by the Hamiltonian H = -  i¡j J |i - j| 1+  si ;sj ; (1) * Corresponding author. Tel.: 385-1-4698801; fax: 385-1-4698889. E-mail address: katarina@vrabac.ifs.hr (K. Uzelac). 0378-4371/02/$-see front matter c  2002 Elsevier Science B.V. All rights reserved. PII:S0378-4371(02)01182-2