Brazilian Journal of Physics

, Volume 47, Issue 2, pp 122–130 | Cite as

A Generalization of Mean Field Theory in a Cluster with Many Sites on the Ising Model from the Bogoliubov Inequality: Hexagonal Nanowire and Nanotube

  • Jander P. Santos
Condensed Matter


A generalization of mean field theory in a cluster with many sites was obtained for the spin-1/2 Ising model from the Gibbs-Bogoliubov inequality. The expressions for the free energy and the magnetization were obtained. The generalization was applied in a structure of the nanowire and nanotube hexagonal lattices, for clusters of seven sites and six sites, respectively. The results for the magnetization, the free energy, the internal energy, the entropy, the specific heat, and the critical frontiers were obtained. The critical temperature and the compensation temperature in a cylindrical Ising nanowire are investigated, in order to clarify the distinction between the ferromagnetic and ferrimagnetic behaviors when the core-shell exchange coupling takes a different sign. The results were compared with other works.


Mean field theory Cluster with many sites Bogoliubov inequality Nanowire/nanotube 


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Copyright information

© Sociedade Brasileira de Física 2016

Authors and Affiliations

  1. 1.Departamento de Matemática and Departamento de Ciências NaturaisUniversidade Federal de São João del-ReiSão João Del ReiBrazil

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