Dipole-dipole minimum energy configuration for Platonic, Archimedean and Catalan solid structures

• Published in: Physics letters. A Vol. 384; no. 36; p. 126916
• Main Authors: Batle, J., Shutov, A.V., Maleev, A.V.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 30.12.2020
• Subjects: Arquimedean and Catalan solids; Classic systems of dipoles; Equilibrium configuration; Minimum total energy; Platonic; Platonic; Equilibrium configuration; Arquimedean and Catalan solids; Classic systems of dipoles; Minimum total energy
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2020.126916

•Systems of classically interacting dipoles are presented, together with energy bounds.•The structures are the Platonic, Archimedean and Catalan solids.•Non-trivial equilibrium structures are studied in full detail for the first time.•Catalan solids are studied from the physical point of view for the first time.•Incommensurate equilibrium dipole angles appear, as well as dipolar structures. 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.