Magnetic Pentagonal Ring - Galois Extensions and Crystallography

M. Labuz; T. Lulek

doi:10.12693/APhysPolA.131.97

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Acta Physica Polonica A

2017 | 132 | 1 | 97-99

Article title

Magnetic Pentagonal Ring - Galois Extensions and Crystallography

Authors

M. Labuz , T. Lulek

Content

http://przyrbwn.icm.edu.pl/APP/PDF/132/app132z1p23.pdf [remote]

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Abstracts

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 ℤ₂×ℤ₂, responsible for extension of the cyclotomic field by the Bethe parameters.

Keywords

75.10.Jm 03.65.Fd 03.67.Lx 02.10.Ud 02.10.De

Publisher

Institute of Physics, Polish Academy of Sciences

Journal

Acta Physica Polonica A

Year

2017

Volume

132

Issue

Pages

97-99

Physical description

Dates

published

2017-07

References

[1] W. Hao, R.I. Nepomechie, A.J. Sommese, Phys. Rev. E 88, 052113 (2013)., doi: 10.1103/PhysRevE.88.052113
[2] J. Milewski, G. Banaszak, T. Lulek, M. Łabuz, R. Stagraczyński, OSID 19, 1250012 (2012)., doi: 10.1142/S1230161212500126
[3] J. Milewski, G. Banaszak, T. Lulek, M. Labuz, Physica B 406, 520 (2011)., doi: 10.1016/j.physb.2010.11.027
[4] H. Bethe, Z. Phys. 71, 205 (1931) (in German, doi: 10.1007/BF01341708
[4a] English translation: D.C. Mattis, The Many-Body Problem, World Sci., Singapore 1993, p. 689., doi: 10.1142/9789812796523
[5] G. Banaszak, B. Lulek, T. Lulek, J. Milewski, B. Szydło, ROMP 71, 205 (2013)., doi: 10.1016/S0034-4877(13)60030-0
[6] S. Lang, Algebra, Addison-Wesley World Student Series, Reading (MA) 1970.
[7] J. Mozrzymas, Applications of Group Theory in Physics, PWN, Warsaw 1977 (in Polish)
[8] J. Mozrzymas, ROMP 6, 29 (1974)., doi: 10.1016/0034-4877(74)90049-4
[8a] J. Mozrzymas, ROMP 6, 83 (1974)., doi: 10.1016/0034-4877(74)90050-0
[9] B. Lulek, T. Lulek, M. Łabuz, R. Stagraczyński, Physica B 405, 2654 (2010)., doi: 10.1016/j.physb.2010.03.043
[10] P. Jakubczyk, A. Wal, D. Jakubczyk, T. Lulek, Comp. Phys. Commun. 183, 1354 (2012)., doi: 10.1016/j.cpc.2012.01.025

Document Type

Publication order reference

YADDA identifier

bwmeta1.element.bwnjournal-article-appv132n1p23kz

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DOI

10.12693/APhysPolA.131.97