立方晶格上硬立方体系统的Phase diagram
Phase diagram of a system of hard cubes on the cubic lattice
摘要：
本文研究了三维立方晶格上$2\times2\times2$硬立方体体系的相图。利用蒙特卡罗模拟，我们表明，该系统表现出四个不同的阶段，作为立方体的密度增加：无序，分层，亚晶格有序，柱状有序。在层状相，该系统自发地分裂成平行的板的大小$2\times L \times L$，其中只有非常小的部分立方体不完全位于板内。在每一个平板内，立方体是无序的;因此，平移对称正好沿着一个主轴被破坏。在类固体亚晶格有序相中，硬立方体优先占据立方晶格的八个亚晶格中的一个，破坏沿所有三个主方向的平移对称性。在柱状相，系统自发地分裂成弱相互作用的平行柱的大小$2\times 2\times L$，其中只有非常小的部分立方体不完全位于列内。在每一列中，系统是无序的，因此平移对称性只在两个主方向上被破坏。利用有限尺寸标度，我们表明，无序分层相变是连续的，而分层亚晶格和亚晶格柱状转变是不连续的。我们构建了一个朗道理论的分层和柱状序参量，这是能够描述的不同阶段，在模拟和过渡的顺序。此外，我们的结果附近的无序分层过渡是一致的$O(3)$普适类受立方各向异性的朗道理论预测。
英文摘要：
We study the phase diagram of a system of $2\times2\times2$ hard cubes on a three dimensional cubic lattice. Using Monte Carlo simulations, we show that the system exhibits four different phases as the density of cubes is increased: disordered, layered, sublattice ordered, and columnar ordered. In the layered phase, the system spontaneously breaks up into parallel slabs of size $2\times L \times L$ where only a very small fraction cubes do not lie wholly within a slab. Within each slab, the cubes are disordered; translation symmetry is thus broken along exactly one principal axis. In the solid-like sublattice ordered phase, the hard cubes preferentially occupy one of eight sublattices of the cubic lattice, breaking translational symmetry along all three principal directions. In the columnar phase, the system spontaneously breaks up into weakly interacting parallel columns of size $2\times 2\times L$ where only a very small fraction cubes do not lie wholly within a column. Within each column, the system is disordered, and thus translational symmetry is broken only along two principal directions. Using finite size scaling, we show that the disordered-layered phase transition is continuous, while the layered-sublattice and sublattice-columnar transitions are discontinuous. We construct a Landau theory written in terms of the layering and columnar order parameters, which is able to describe the different phases that are observed in the simulations and the order of the transitions. Additionally, our results near the disordered-layered transition are consistent with the $O(3)$ universality class perturbed by cubic anisotropy as predicted by the Landau theory.
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