二聚体库仑分子晶体基态的三临界性
Tricriticality for dimeric Coulomb molecular crystals in ground state
摘要：
研究了二聚体系统的基态性质。每个二聚体由一对固定距离的等效电荷组成，浸没在中和均匀的背景中。所有的电荷通过库仑势相互作用。二聚体中心形成具有纵横比$α\in [0,1]$的二维矩形晶格，并且允许每个二聚体围绕其中心旋转。以前的数值模拟，为更一般的汤川相互作用，表明只有两个基本的二聚体配置可以出现：要么所有的二聚体是平行的，或者他们有两个不同的角度取向交替（棋盘格）子晶格。随着二聚体尺寸的增加，两个二级相变，有关的两种对称性破缺的二聚体的取向，报告。在本文中，我们使用最近的分析方法的基础上扩展的相互作用能Misra功能，收敛速度快，并提供了一个分析推导的临界行为。我们的主要结果是，存在一个特定的纵横比的矩形晶格$α^*=0.71410684000071\ldots$的划分模型的相空间到两个不同的区域。如果晶格纵横比为$α>α^*$，我们恢复了这两种类型的二级相变，发现它们都是临界指数为$β= 1/2$的平均场型相变。若为$α<α^*$，则与交替亚晶格上二聚体角度不连续相关的相变变为一级相变。对于$α=α^*$，一阶和二阶相变在三临界点相遇，其特征在于不同的临界指数$β= 1/4$。这种现象是已知的文献中的朗道理论的一个组成部分的领域，但在我们的两个组成部分的版本的情况更加复杂。
英文摘要：
We study the ground-state properties of a system of dimers. Each dimer consists in a pair of equivalent charges at a fixed distance, immersed in a neutralizing homogeneous background. All charges interact pairwisely by Coulomb potential. The dimer centers form a two-dimensional rectangular lattice with the aspect ratio $α\in [0,1]$ and each dimer is allowed to rotate around its center. The previous numerical simulations, made for the more general Yukawa interaction, indicate that only two basic dimer configurations can appear: either all dimers are parallel or they have two different angle orientations within alternating (checkerboard) sublattices. As the dimer size increases, two second-order phase transitions, related to two kinds of the symmetry breaking in dimer's orientations, were reported. In this paper, we use a recent analytic method based on an expansion of the interaction energy in Misra functions which converges quickly and provides an analytic derivation of the critical behaviour. Our main result is that there exists a specific aspect ratio of the rectangular lattice $α^*=0.71410684000071\ldots$ which divides the space of model's phases onto two distinct regions. If the lattice aspect ratio $α>α^*$, we recover both types of the second-order phase transitions and find that they are of mean-field type with the critical exponent $β= 1/2$. If $α<α^*$, the phase transition associated with the discontinuity of dimer's angles on alternating sublattices becomes of first order. For $α=α^*$, the first- and second-order phase transitions meet at the tricritical point, characterized by the different critical index $β= 1/4$. Such phenomenon is known from literature about the Landau theory of one-component fields, but in our two-component version the scenario is more complicated.
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