Self-consistent field near the critical point in the Ising antiferromagnetic model

V. Ya. Krivnov ; O. A. Ol'khov ; B. N. Provotorov ; M. E. Sarychev

Teoretičeskaâ i matematičeskaâ fizika, Tome 2 (1970) no. 2, pp. 244-253

Résumé

On the basis of physical considerations, a class of diagrams governing the thermodynamic behavior of the fsing antiferromagnetic and ferromagnetic models in the critical domain for $T$ ($T_{\text к}$ is the critical temperature) for the case of nearest neighbor interaction is mentioned. The nature of the singularity for antiferromagnetic susceptibility is determined by summing these diagrams, and also for the polarization, specific heat, and susceptibility in the ferromagnetic case. The domain of critical behavior $z^{-2}(T_{\text к}-T)/T_{\text к}$ ($z$ is the number of nearest neighbors) is also determined for the ferromagnetic case. A method is mentioned for reconstructing the diagram series to permit a correct determination of the critical temperature. Summation of the diagrams results in a transcendental equation, and specific results are obtained by solving it numerically. The volume of calculations needed to compute the critical behavior in the proposed method is considerably less than for computations based on an analysis of high- and low-temperature expansions. The results obtained agree with experimental results and with those found numerically.