类水格子气模型密度反常的有限格点和唯象近似
Finite Lattice and Phenomenological Approximations for the Anomaly in the Density of a Water-like Lattice Gas Model
摘要：
我们提出了一个模型的二维，缔合水状格子气与一个单一的变量代表长距离和短距离的相互作用。在有限格点上用状态计数法精确求解相应的哈密顿量，从而得到配分函数的解析表达式。晶格尺寸的选择是基于几何特征的稳定阶段，在以前的工作中发现使用蒙特卡罗模拟。得到了有限晶格中粒子密度的表达式，并在相图中给出了密度异常区的共存曲线。最后，提出了系统密度的唯象理论，并与以前的结果进行了比较。
英文摘要：
We propose a model for a two dimensional, associative water-like lattice gas with one single variable representing both long and short-range interactions. The corresponding hamiltonian was solved exactly, by state enumeration in a finite lattice, so to obtain an analytic expression for the partition function. The lattice dimensions were chosen based on geometric characteristics of the stable phases found in previous works using Monte Carlo simulations. An expression for the particle density in the finite lattice was then obtained, and coexistence curves with a region of anomaly in the density presented in a phase diagram. In the end, a phenomenological theory for the system density is proposed and compared to the previous results.
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