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Minimum energy configurations for interacting dipoles in simple hypercubic lattices
Results in Physics ( IF 5.3 ) Pub Date : 2020-04-29 , DOI: 10.1016/j.rinp.2020.103114
J. Batle

Systems consisting of dipoles owe their properties to the specific nature of the dipole-dipole interaction. Usually this form of interaction is intended for systems in three dimensions, although in several instances it can be reduced to 2+ dimensions. Their study is relevant because under certain conditions, such as large dipole moments or low temperatures, the classical approach is still valid in quantum systems. In the present work, we shall study systems of particles possessing a dipole moment arranged beyond the two-dimensional (three-dimensional) simple square (simple cubic) lattice. That is, we shall i) find the equilibrium configuration for dipoles in extended hypercubic lattices, and ii) compute the concomitant minimum energy per dipole in the bulk. Our approach shall not resort to any Ewald summation technique, is completely general and can be extended to any periodic geometric configuration. The corresponding results imply a slightly exponential scaling of the energy in terms of the dimension D itself.



中文翻译:

简单超三次晶格中与偶极子相互作用的最小能量构型

由偶极子组成的系统的性质归因于偶极子-偶极子相互作用的特定性质。通常,这种形式的交互旨在用于三个维度的系统,尽管在某些情况下可以减少为2+尺寸。他们的研究是有意义的,因为在某些条件下,例如大偶极矩或低温,经典方法在量子系统中仍然有效。在本工作中,我们将研究具有偶极矩的粒子系统,这些粒子的偶极矩布置在二维(三维)简单正方形(简单立方)晶格之外。也就是说,我们将i)在扩展的超三次晶格中找到偶极子的平衡构型,并且ii)计算体中每个偶极子的伴随最小能量。我们的方法不得求助于任何Ewald求和技术,它是完全通用的,可以扩展到任何周期性的几何构造。相应的结果意味着能量在尺寸D本身方面呈指数级缩放。

更新日期:2020-04-29
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