Numerical test of finite-size scaling predictions for the droplet condensation-evaporation transition

Andreas Nuβbaumer,Elmar Bittner,Wolfhard Janke,Johannes Zierenberg

doi:10.1088/1742-6596/759/1/012009

Abstract

We numerically study the finite-size droplet condensation-evaporation transition in two dimensions. We consider and compare two orthogonal approaches, namely at fixed temperature and at fixed density, making use of parallel multicanonical simulations. The equivalence between Ising model and lattice gas allows us to compare to analytical predictions. We recover the known background density (at fixed temperature) and transition temperature (at fixed density) in the thermodynamic limit and compare our finite-size deviations to the predicted leading-order finite-size corrections.

Highlights

Droplet formation is an essential process in nature with a variety of analogues in biological systems and material science
The resulting theory has been supported by numerous computational studies at fixed temperature, including the two-dimensional lattice gas [6, 7, 8] and three-dimensional Lennard-Jones gas [9, 10, 11]
In order to ensure ergodic sampling, we augmented the Kawasaki Monte Carlo update with a multicanonical scheme to locally sample a flat histogram including transition states and ensuring a good sampling of the energy probability distribution up to suppressions of 30 orders of magnitude

Summary

Introduction

Droplet formation is an essential process in nature with a variety of analogues in biological systems and material science. This generally involves non-equilibrium processes, e.g., the formation of nucleation prerequisites from local fluctuations while the surrounding gas acts as a density bath. The resulting theory has been supported by numerous computational studies at fixed temperature, including the two-dimensional lattice gas [6, 7, 8] and three-dimensional Lennard-Jones gas [9, 10, 11]. The orthogonal approach at fixed density has received less attention [12], but recently enabled us to come closer to the asymptotic scaling regime for two- and three-dimensional lattice gas and three-dimensional Lennard-Jones gas [13]. We will compare the leading-order scaling corrections for a two-dimensional lattice gas at fixed temperature and fixed density from analytical predictions with numerical results

Methods

Results

Conclusion