Phase diagram和Yukawa双层膜的临界性质
Phase diagram and critical properties of Yukawa bilayers
摘要：
本文研究了在无量纲距离为$η$的两个平行硬壁表面上，具有Yukawa相互作用的点状粒子的基态Wigner双层。该模型包括作为限制情况的未屏蔽库仑势和硬球。由Messina和Löwen数值研究的Yukawa粒子的相图[Phys. Rev. Lett. 91（2003）146101]，当$η$从0变化到中间值时，表现出五个不同的交错相位。我们提出了一个晶格求和方法，使用广义Misra函数，使我们能够计算每个粒子的相的能量，精度比通常在计算机模拟高得多。这使我们能够处理相图的一些微小细节。从六方相I到相II显示发生在$η=0$，这解决了长期的争议。我们发现一个三临界点，墨西拿和Löwen建议的共存域的几个阶段，建议划分交错的菱形相成两个独立的区域。我们的计算揭示了一个连续的区域，这个菱形相与一个非常狭窄的连接通道。进一步证明了所有的二阶相变都是平均场型的。我们还得到了渐近形状的临界线接近库仑和硬球极限。在硬球极限和接近硬球极限时，精确地确定了当前相的内部参数对$η$的依赖关系。
英文摘要：
We study the ground-state Wigner bilayers of pointlike particles with Yukawa pairwise interactions, confined to the surface of two parallel hard walls at dimensionless distance $η$. The model involves as limiting cases the unscreened Coulomb potential and hard spheres. The phase diagram of Yukawa particles, studied numerically by Messina and Löwen [Phys. Rev. Lett. 91 (2003) 146101], exhibits five different staggered phases as $η$ varies from 0 to intermediate values. We present a lattice summation method using the generalized Misra functions which permits us to calculate the energy per particle of the phases with a precision much higher than usual in computer simulations. This allows us to address some tiny details of the phase diagram. Going from the hexagonal phase I to phase II is shown to occur at $η=0$, which resolves a longtime controversy. We find a tricritical point where Messina and Löwen suggested a coexistence domain of several phases which was suggested to divide the staggered rhombic phase into two separate regions. Our calculations reveal one continuous region for this rhombic phase with a very narrow connecting channel. Further we show that all second-order phase transitions are of mean-field type. We also derive the asymptotic shape of critical lines close to the Coulomb and hard-spheres limits. In and close to the hard-spheres limit, the dependence of the internal parameters of the present phases on $η$ is determined exactly.
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