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

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.

Automated summary

This study compares different paths to the critical temperature when approaching the critical composition in a symmetric binary liquid, utilizing finite-size scaling analysis and simulations. It is found that for open systems and sub-volumes with boundary interference, the use of a two-parameter finite-size scaling method can address the difficulties present.