Magnetic Pentagonal Ring - Galois Extensions and Crystallography |

M. Labuz
^{a} and T. Lulek^{b,c}^{a}Department of Theoretical Physics, Faculty of Mathematics and Natural Sciences, University of Rzeszów;, S. Pigonia 1, 35-310 Rzeszów, Poland
^{b}Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
^{c}Department of Experimental Physics, Faculty of Mathematics and Natural Sciences, University of Rzeszów, S. Pigonia 1, 35-310 Rzeszów, Poland |

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The Galois symmetry of exact Bethe Ansatz eigenstates for magnetic pentagonal ring is shown to bear a close analogy to some crystallographic constructions. Automorphisms of number field extensions associated with these eigenstates prove to be related to choices of the Bravais cells in the finite crystal lattice ℤ_{2}×ℤ_{2}, responsible for extension of the cyclotomic field by the Bethe parameters. |

DOI: 10.12693/APhysPolA.132.97 PACS numbers: 75.10.Jm, 03.65.Fd, 03.67.Lx, 02.10.Ud, 02.10.De |