A Generalization of Mean Field Theory in a Cluster with Many Sites on the Ising Model from the Bogoliubov Inequality: Hexagonal Nanowire and Nanotube
- 115 Downloads
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.
KeywordsMean field theory Cluster with many sites Bogoliubov inequality Nanowire/nanotube
- 5.N.N. Jr. Bogoliubov, Quantum Statistical Mechanics: Selected Works of N. N. Bogoliubov (World Scientific, Singapore, 2015)Google Scholar
- 9.L.A. Maksimov, A.L. Kuzemsky, To the theory of ferromagnetic crystal with two spins per site. Fiz. Met. Metalloved. 31, 5 (1971)Google Scholar
- 39.L. Neél, Magnetic properties of ferrites: ferrimagnetism and antiferromagnetism. Anneles de Physique. 3, 137 (1948)Google Scholar
- 40.T. Kaneyoshi, Magnetism, Introduction to Surface (CRC Press, Boca Raton FL, 1991)Google Scholar