Continuous Demixing Transition of Binary Liquids: Finite-Size Scaling from the Analysis of Sub-Systems

Abstract

A binary liquid near its consolute point exhibits critical fluctuations of local composition and a diverging correlation length. The method of choice to calculate critical points in the phase diagram is a finite-size scaling analysis, based on a sequence of simulations with widely different system sizes. Modern, massively parallel hardware facilitates that instead cubic sub-systems of one large simulation are used. Here, this alternative is applied to a symmetric binary liquid at critical composition and different routes to the critical temperature are compared: 1) fitting critical divergences of the composition structure factor, 2) scaling of fluctuations in sub-volumes, and 3) applying the cumulant intersection criterion to sub-systems. For the last route, two difficulties arise: sub-volumes are open systems, for which no precise estimate of the critical Binder cumulant Uc is available. Second, the boundaries of the simulation box interfere with the sub-volumes, which is resolved here by a two-parameter finite-size scaling. The implied modification to the data analysis restores the common intersection point, yielding Uc=0.201 +/- 0.001, universal for cubic Ising-like systems with free boundaries. Confluent corrections to scaling, which arise for small sub-system sizes, are quantified and the data are compatible with the universal correction exponent omega approximate to 0.83.