Application of the Bogoliubov inequality in the Ising model

Zhou JianHua, Yang ChuanZhang

A transverse Ising model for a magnetic superlattice of spin-1/2 Ising layered media intercalated by periodic interfaces described by the spin-1/2 Ising model is considered. Phase diagrams and different profiles of magnetization determined by the parameters of the model are discussed within a variational procedure based on Bogoliubov's inequality for the free energy. Our results agree to those of the other's work at the limit of .

George Allen Baker Jr., Jerome J. Erpenbeck

A. F. S. Moreira, W. Figueiredo

A semi-infinite compressible Ising model is studied within a variational approach based on Bogoliubov's inequality. The exchange couplings in our effective-spin Hamiltonian depend on external forces. We have determined the profile of the magnetization and the phase diagram for the surface critical couplings as a function of the external force.

David A. Lavis, G. M. Bell

Dalton A R Sakthivadivel

In this set of notes, a complete, pedagogical tutorial for applying mean field theory to the two-dimensional Ising model is presented. Beginning with the motivation and basis for mean field theory, we formally derive the Bogoliubov inequality and discuss mean field theory itself. We proceed with the use of mean field theory to determine a magnetisation function, and the results of the derivation are interpreted graphically, physically, and mathematically. We give a new interpretation of the self-consistency condition in terms of intersecting surfaces and constrained solution sets. We also include some more general comments on the thermodynamics of the phase transition. We end by evaluating symmetry considerations in magnetisation, and some more subtle features of the Ising model. Together, a self-contained overview of the mean field Ising model is given, with some novel presentation of important results.

H Ulman, M Athematics J Ournal