Dipole-dipole minimum energy configuration for Platonic,Archimedean and Catalan solid structures |
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Institution: | 1. Departament de Física, Universitat de les Illes Balears, 07122 Palma de Mallorca, Balearic Islands, Spain;2. Department of Computer Engineering, Vladimir State University, 87 Gorkiy str., Vladimir 600000, Russia;3. Department of General and Theoretical Physics, Vladimir State University, 87 Gorkiy str., Vladimir 600000, Russia |
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Abstract: | Several magnetic materials consisting of dipoles owe their properties to the specific nature of the dipole-dipole interaction. In the present work, we study systems of dipoles where the particles are arranged on various types of three-dimensional structures. However, these solids are not arbitrary. They constitute the well-known Platonic, Archimedean and Catalan solids. We systematically study them in order to fill a gap in the literature that does not contemplate this interaction in the previous solids, despite the fact that they are encountered in many different physical systems. In particular, in the regime of strong dipole moments where a classical treatment is possible, we shall provide not only the minimum energy but also the precise orientations of all their dipoles. We will numerically obtain the minimum energy configuration where all vertices possess the same classic dipole, either electric or magnetic. |
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Keywords: | Classic systems of dipoles Equilibrium configuration Minimum total energy Platonic Arquimedean and Catalan solids |
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