论文标题
从硬球到硬核旋转
From hard spheres to hard-core spins
论文作者
论文摘要
硬球系统表现出仅由其密度控制的物理。之所以出现，是因为相互作用的能量是无限或零，因此所有允许的配置都具有完全相同的能量。低密度相是液体，而高密度相是晶体，这是“按疾病的秩序”的一个例子，因为它纯粹是由熵考虑的。在这里，我们研究了一个硬旋模模型的家族，我们称之为铁杆旋转模型，在这里我们用晶格自由的定向自由度代替了硬球自由度。他们的硬核交互方式类似地将许多自旋系统的配置分为允许和不允许的扇区。我们为一组具有$ \ Mathbb {z} _n $对称的模型的方形晶格介绍了$ d = 2 $的详细结果，该模型概括了potts型号及其$ u（1）$限制，用于铁磁性和抗firomagnetic and Antantectic and Antantectic and Antyantic Mentaction，我们将其称为排除和包含模型。随着排除/包含角度的变化，我们发现无序相位和具有准长序列的有序相之间的kosterlitz-无效的相位过渡，这是这些系统中的疾病的形式顺序。这些结果源于一组高度表示，一种沿子簇算法和转移矩阵计算。
A system of hard spheres exhibits physics that is controlled only by their density. This comes about because the interaction energy is either infinite or zero, so all allowed configurations have exactly the same energy. The low density phase is liquid, while the high density phase is crystalline, an example of "order by disorder" as it is driven purely by entropic considerations. Here we study a family of hard spin models, which we call hardcore spin models, where we replace the translational degrees of freedom of hard spheres with the orientational degrees of freedom of lattice spins. Their hardcore interaction serves analogously to divide configurations of the many spin system into allowed and disallowed sectors. We present detailed results on the square lattice in $d=2$ for a set of models with $\mathbb{Z}_n$ symmetry, which generalize Potts models, and their $U(1)$ limits, for ferromagnetic and antiferromagnetic senses of the interaction, which we refer to as exclusion and inclusion models. As the exclusion/inclusion angles are varied, we find a Kosterlitz-Thouless phase transition between a disordered phase and an ordered phase with quasi-long-ranged order, which is the form order by disorder takes in these systems. These results follow from a set of height representations, an ergodic cluster algorithm, and transfer matrix calculations.
