Continuous Demixing Transition of Binary Liquids: Finite‐Size Scaling from the Analysis of Sub‐Systems. Issue 4 (28th January 2021) - Pathania, Yogyata; Chakraborty, Dipanjan; Höfling, Felix
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 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 c = 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 ω ≈ 0.83 . Abstract : Decomposing a large simulation box into equally sized, open sub‐systems provides simultaneous access to a range of sub‐system sizes ℓ, allowing for conventional finite‐size scaling analyses of the susceptibility (top) and the Binder cumulant (bottom). Corrections to scaling arise for large sub‐system sizes due to the finite simulation box and can be accounted for in a two‐parameter scaling ansatz.