标题： 一维自引力格子气体模型的微正则蒙特卡罗研究 显示英文标题

标题： Microcanonical Monte Carlo Study of One Dimensional Self-Gravitating Lattice Gas Models

摘要： 在本研究中，我们对一维自引力玩具模型进行了微正则蒙特卡罗研究。我们研究了硬核势的影响，并将其结果与使用软化参数的结果以及模型几何结构的影响进行比较。为了研究系统中几何结构和边界的影响，我们引入了一个具有直线运动对称性的模型，而不是圆环，我们将其称为$1/r$模型。硬核粒子势引入了粒子大小的影响，从而引入了系统密度的影响，该密度重新定义为系统的填充分数。后者在软化粒子的情况下起到类似于软化参数$\epsilon$的作用。在低填充分数的情况下，具有硬核粒子的模型表现出保持三维引力系统内在特性的行为，例如负比热。对于较高的填充分数，环状系统的行为类似于哈密顿平均场模型，而对于$1/r$则类似于一维系统。 显示英文摘要

摘要： In this study we present a Microcanonical Monte Carlo investigation of one dimensional self-gravitating toy models. We study the effect of hard-core potentials and compare to those results obtained with softening parameters and also the effect of the geometry of the models. In order to study the effect of the geometry and the borders in the system we introduce a model with the symmetry of motion in a line instead of a circle, which we denominate as $1/r$ model. The hard-core particle potential introduces the effect of the size of particles and, consequently, the effect of the density of the system that is redefined in terms of the packing fraction of the system. The latter plays a role similar to the softening parameter $\epsilon$ in the softened particles' case. In the case of low packing fractions both models with hard-core particles show a behavior that keeps the intrinsic properties of the three dimensional gravitational systems such as negative heat capacity. For higher values of the packing fraction the ring the system behaves as the Hamiltonian Mean Field model and while for the $1/r$ it is similar to the one-dimensional systems.