Weakly Periodic Gibbs Measures of the Ising Model on the Cayley Tree of Order Five and Six

  • Nasir Ganikhodjaev
  • Muzaffar Rahmatullaev
  • Mohd Hirzie Bin Mohd Rodzhan
Article
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Abstract

For Ising model on the Cayley tree of order five and six we present new weakly periodic (non-periodic) Gibbs measures corresponding to normal subgroups of indices two in the group representation of the Cayley tree.

Keywords

Cayley tree Gibbs measure Ising model Weakly periodic measure 

Mathematics Subject Classification (2010)

82B20 

Notes

Acknowledgments

This research was supported by Ministry of Higher Education Malaysia (MOHE) under grant FRGS 14-116-0357. Second author Rahmatullaev Muzaffar thanks IIUM for providing financial support (grant FRGS 14-116-0357) and all facilities.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  • Nasir Ganikhodjaev
    • 1
  • Muzaffar Rahmatullaev
    • 2
  • Mohd Hirzie Bin Mohd Rodzhan
    • 1
  1. 1.Department of Computational and Theoretical Sciences, Faculty of ScienceInternational Islamic University MalaysiaKuantanMalaysia
  2. 2.Institute of MathematicsNational University of UzbekistanTashkentUzbekistan

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