Exploring different regimes in finite-size scaling of the droplet condensation-evaporation transition

TL;DR

This paper conducts a finite-size scaling analysis of droplet condensation-evaporation transitions in lattice and Lennard-Jones gases, revealing a crossover from intermediate to large-system behavior and emphasizing the importance of scaling range considerations.

Contribution

It introduces an analysis of intermediate scaling regimes and higher-order corrections, providing insights into finite-size effects in phase transition studies.

Findings

Verification of leading-order scaling predictions for transition temperature

Identification of an intermediate scaling regime with crossover behavior

Implications for accurate thermodynamic limit predictions

Abstract

We present a finite-size scaling analysis of the droplet condensation-evaporation transition of a lattice gas (in two and three dimensions) and a Lennard-Jones gas (in three dimensions) at fixed density. Parallel multicanonical simulations allow sampling of the required system sizes with precise equilibrium estimates. In the limit of large systems, we verify the theoretical leading-order scaling prediction for both the transition temperature and the finite-size rounding. In addition, we present an emerging intermediate scaling regime, consistent in all considered cases and with similar recent observations for polymer aggregation. While the intermediate regime locally may show a different effective scaling, we show that it is a gradual crossover to the large-system scaling behavior by including empirical higher-order corrections. This implies that care has to be taken when considering scaling ranges, possibly leading to completely wrong predictions for the thermodynamic limit. In this study, we consider a crossing of the phase boundary orthogonal to the usual fixed temperature studies. We show that this is an equivalent approach and, under certain conditions, may show smaller finite-size corrections.