Finite-size effects and approach to criticality in Gibbs ensemble simulations

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Abstract
We have performed Monte Carlo simulations in the Gibbs ensemble for symmetric square-well fluids that exhibit liquid-liquid immiscibility, in order to investigate finite size-effects and the approach to criticality for systems described by continuous potentials. The square-well mixture was studied in two and three dimensions, following the methodology of Mon and Binder. A strong finite-size effect is seen for both two- and three-dimensional systems, with the critical temperature overestimated by several per cent even for system sizes in excess of 1000 particles. Even away from the critical point, the composition of the coexisting phases is a function of system size. This contrasts sharply to the observed vapour-liquid phase behaviour of the pure Lennard-Jones system, which does not exhibit strong finite-size effects. A crossover from non-classical to classical exponents as the critical point is approached is observed for the two-dimensional systems, as previously seen by Mon and Binder for the Ising model. No crossover to classical behaviour was observed for the three-dimensional square-well system.