Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom.
J Chem Phys. 2010 Feb 21;132(7):074111. doi: 10.1063/1.3316208.
The symmetrical restricted Gibbs ensemble (RGE) is a version of the Gibbs ensemble in which particles are exchanged between two boxes of fixed equal volumes. It has recently come to prominence because--when combined with specialized algorithms--it provides for the study of near-coexistence density fluctuations in highly size-asymmetric binary mixtures. Hitherto, however, a detailed framework for extracting accurate estimates of critical point and coexistence curve parameters from RGE density fluctuations has been lacking. Here we address this problem by exploiting an exact link between the RGE density fluctuations and those of the grand canonical ensemble. In the subcritical region we propose and test a simple method for obtaining accurate estimates of coexistence densities. In the critical region we identify an observable that serves as a finite system size estimator for the critical point parameters, and present a finite-size scaling theory that allows extrapolation to the thermodynamic limit.
对称限制吉布斯系综（RGE）是吉布斯系综的一个版本，其中粒子在两个固定等体积的盒子之间交换。由于它与专门的算法相结合，可以研究高度尺寸不对称的二元混合物中接近共存的密度涨落，因此最近引起了人们的关注。然而，迄今为止，从 RGE 密度涨落中提取临界点和共存曲线参数的准确估计值的详细框架一直缺乏。在这里，我们通过利用 RGE 密度涨落与巨正则系综密度涨落之间的精确关系来解决这个问题。在亚临界区域，我们提出并测试了一种简单的方法，可用于准确估计共存密度。在临界区域，我们确定了一个可观察量，作为临界点参数的有限系统尺寸估计器，并提出了一个有限尺寸标度理论，允许外推到热力学极限。
