Lattice Fundamental Measure Theory Beyond 0D Cavities: Dimers on Square Lattices

IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Michael Zimmermann, Martin Oettel
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引用次数: 0

Abstract

Using classical density functional theory, we study the behavior of dimers, i.e. hard rods of length \(L=2\), on a two-dimensional cubic lattice. For deriving a free energy functional, we employ Levy’s prescription which is based on the minimization of a microscopic free energy with respect to the many-body probability under the constraint of a fixed density profile. Using that, we recover the "0D cavity" functional originally found by Lafuente and Cuesta and derive an extension by applying a more general "cluster density functional theory" method introduced by Lafuente and Cuesta as well. Moreover, we introduce a new free energy functional, which is based on approximated configurational probabilities. Both derived free energy functionals are exact on cavities that can hold at most two particles simultaneously. The first functional allows to improve the prediction of the free energy in bulk and both of them improve the prediction in highly confined systems, especially for high packing fractions, in comparison to the "0D cavity" functional.

超越 0D 空腔的晶格基本量度理论:方格上的二聚体
利用经典密度泛函理论,我们研究了二聚体(即长度为 \(L=2\)的硬棒)在二维立方晶格上的行为。为了推导自由能函数,我们采用了列维处方,该处方基于在固定密度曲线约束下与多体概率有关的微观自由能最小化。利用这一方法,我们恢复了拉富恩特和奎斯塔最初发现的 "0D空穴 "函数,并通过应用拉富恩特和奎斯塔引入的更通用的 "簇密度泛函理论 "方法得到了扩展。此外,我们还引入了一种基于近似构型概率的新自由能函数。在最多可同时容纳两个粒子的空穴上,这两种推导出的自由能函数都是精确的。与 "0D空穴 "函数相比,第一个函数可以改进对体态自由能的预测,而这两个函数都可以改进对高度约束系统的预测,特别是对高堆积分数的预测。
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来源期刊
Journal of Statistical Physics
Journal of Statistical Physics 物理-物理:数学物理
CiteScore
3.10
自引率
12.50%
发文量
152
审稿时长
3-6 weeks
期刊介绍: The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.
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