可穿透粒子二组分系统格子气模型的热力学坍缩
Thermodynamic collapse in a lattice-gas model for a two-component system of penetrable particles
摘要：
我们研究了正方形晶格衬底上具有同位置和最近邻相互作用的可穿透粒子的格子气模型。穿透性意味着占据单个晶格位置的粒子数量是无限的，并且模型本身旨在作为现实软物质系统中遇到的可穿透粒子的简单表示。我们的具体重点是在一个二元混合物，其中粒子的相同的物种排斥和那些相反的物种相互吸引。由于渗透性和每个位点的无限占据，系统表现出热力学崩溃，这在模拟中表现为分散在整个系统中的极其密集的簇的出现，具有簇$E\propto -n^2$的能量，其中$n$是簇中的粒子数。将粒子系统转化为自旋系统后，在大密度极限下，哈密顿量恢复为简谐形式，导致过去用于模拟界面粗糙化过渡的离散高斯模型。对于有限密度，由于存在一个非调和项，系统近似使用变分高斯模型。
英文摘要：
We study a lattice-gas model of penetrable particles on a square-lattice substrate with same-site and nearest-neighbor interactions. Penetrability implies that the number of particles occupying a single lattice site is unlimited and the model itself is intended as a simple representation of penetrable particles encountered in realistic soft-matter systems. Our specific focus is on a binary mixture, where particles of the same species repel and those of the opposite species attract each other. As a consequence of penetrability and the unlimited occupation of each site, the system exhibits thermodynamic collapse, which in simulations is manifested by an emergence of extremely dense clusters scattered throughout the system with energy of a cluster $E\propto -n^2$ where $n$ is the number of particles in a cluster. After transforming a particle system into a spin system, in the large density limit the Hamiltonian recovers a simple harmonic form, resulting in the discrete Gaussian model used in the past to model the roughening transition of interfaces. For finite densities, due to the presence of a non-harmonic term, the system is approximated using a variational Gaussian model.
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