# Publication in Advanced Theory & Simulation

The demixing transition of a binary liquid can be located from the sub-system analysis of a large simulation

News from Feb 01, 2021

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 *U _{c}* 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

*U*=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

_{c}*ω*≈0.83.

*Publication:*

Y. Pathania, D. Chakraborty, and F. Höfling,*Continuous Demixing Transition of Binary Liquids: Finite‐Size Scaling from the Analysis of Sub‐Systems,*Adv. Theory Simul., 202000235 (2021).