In this approximation, the dependences of the magnetization and Curie temperature on the concentration of magnetic atoms for the Ising model with mobile nonmagnetic impurities have been constructed and the limiting concentrations of the appearance of spontaneous magnetization in the ground state have been...
It is shown that the decoupling approximation in functional integral method,which has been used by Hasegawa, leads to a generalized Ising model in itinerant-electron s>'sterns, and then a new theorv to gO be>'ond the sinsle-site ar>rroximationis proposed. It is based on the Bethe approx...
The paper offers an interpretation of Bethe approximation based on comparison of spin clusters of different sizes on the Cayley tree. Based on this interpretation, the authors suggested the method to construct Bethe approximation for the node- or bond-diluted Ising magnet. The method provides an ...
The Bethe lattice is an in,nite graph,where any two points are connected by a single path and each vertex has the same number of branches Z, as shown in Fig. 1for Z=4.The name “Bethe lattice” originates from the fact that Bethe’s approximation for the Ising model is ex-act ...
To this end, we write the overlap between two wave functions within the Bethe approximation which allows us to replace the global orthogonality constraint with some local constraints on the variational parameters. The method is applied to the transverse Ising model and different levels of ...
In the Bethe lattice in which the Bethe approximation is exact, the Curie temperatures of the Ising model with spin \includegraphics{dummy.eps} are obtained exactly by generalizing the method of Katsura and Takizawa for the system with \includegraphics{dummy.eps}. This method is applied to the...
We study the random Ising model in the pair approximation of the cluster variation method. We show that the distribution function of the effective field is determined either by a reducibility condition of the distribution function of two sites to that of one site or by a stationarity condition ...
relationfunctionoftheIsingmodelontheselattices,isdirectlyrelatedwiththecorrespondingquantityintheBethe andtheWeissapproximation,respectively. IthasbeenshownthatifthermodynamicpropertiesinfiniteCayleytreeontheRiemannsheets,theBethe oftheIsingmodelonaninfiniteCayleytreearecalcu-lattice.TheBethelatticehasthesamecoordination ...
The XXZ model on the Bethe lattice undergoes a first-order quantum phase transition at the isotropic point. Furthermore, the simple update scheme is found to be related with the Bethe approximation. Finally, by applying the simple update to various tree tensor clusters, we can obtain rather ...
After the introductionof the BEG model, it has been studied for numerous purposes bythe use of many techniques. Some of them are considered in thespin-1 Ising model as follows:An arbitrary bilinear and biquadratic pair interactions wasstudied in the molecular-field approximation by using one- ...