Monte Carlo study of finite-size effects at a weakly first-order phase transition

A new kind of finite-size phenomenon in the five-state Potts model in two dimensions, a ‘‘false’’ ground state, was recently reported by Katznelson and Lauwers based on Monte Carlo studies of large lattices. We reexamine the behavior of this weakly first-order system by performing extensive Monte Carlo simulations, and demonstrate that the ‘‘novel’’ states previously observed in internal-energy-distribution histograms tend to disappear when runs of sufficient length are used. We present evidence that very strong critical slowing down and a pseudodivergent correlation length are responsible for the observed effects. Our additional analysis of finite-size effects in the ten-state Potts model on small lattices (L≤10) shows a crossover of scaling from $L^{\mathrm{-}d}$ behavior (observed earlier on larger lattices) to a nonanalytic form. This result is used to discuss the observed nonanalytic scaling of thermodynamic quantities in the five-state Potts model.