Mean Field Study of a New Nanotube Structure from a Double Hexagonal Symmetry

  • S. Naji
  • S. Ziti
  • A. Belhaj
  • H. Labrim
  • L. Bahmad
  • A. Benyoussef
  • A. El Kenz
  • L. Laânab
Original Paper


Borrowing ideas from Lie algebras, we propose a new nanotube model based on a double hexagonal geometry appearing in the G 2 Lie symmetry. This structure involves two hexagons of unequal side length at angle 30 producing \((\sqrt {3}~\times ~\sqrt {3})R30~^{\circ }\) and (1 × 1) geometries. In this configuration system, the principal unit cell contains 12 sites instead of only 6 ones, arising in the single hexagonal structure on which the graphene-like models are based. More precisely, we engineer a superlattice model based on periodic bilayers consisting of particles with the spins \(\sigma =\pm \frac {1}{2}\) having two possible states, placed at sites of the double hexagonal structure. Then, we investigate the phase diagrams and the magnetic properties using the mean field method. In particular, we find six stable phases required by a global Z 2 symmetry associated with the spin values placed at the site of the G 2 double hexagonal structure.


G2 Lie symmetry Nanotube Phase diagrams and critical temperature Mean field method. 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • S. Naji
    • 1
    • 2
  • S. Ziti
    • 3
  • A. Belhaj
    • 4
  • H. Labrim
    • 5
  • L. Bahmad
    • 1
  • A. Benyoussef
    • 1
    • 6
    • 7
  • A. El Kenz
    • 1
  • L. Laânab
    • 8
  1. 1.Laboratoire de Magnétisme et Physique des Hautes Énergies (LMPHE-URAC 12) Faculté des SciencesUniversité Mohammed V-AgdalRabatMorocco
  2. 2.Department of Physics, Faculty of ScienceIbb UniversityIbbYemen
  3. 3.Department of Computer Sciences, Faculty of SciencesUniversity Mohammed V-AgdalRabatMorocco
  4. 4.Département de Physique, Faculté PolydisciplinaireUniversité Sultan Moulay Slimane Béni MellalBéni MellalMorocco
  5. 5.Centre National de l’Energie, des Sciences et des Techniques NucléairesRabatMorocco
  6. 6.Institute of Nanomaterials and Nanotechnology MAScIRRabatMorocco
  7. 7.Hassan II Academy of Science and TechnologyRabatMorocco
  8. 8.Laboratoire Conception et Systèmes, Faculté des SciencesUniversité Mohammed V-AgdalRabatMorocco

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