Statistical Theory of Binary Alloys. II. Application to Ferromagnetism

Abstract

Using the general free energy formula of binary alloys discussed in the preceding, paper, ⁽¹⁾ the magnetie and thermal properties of the so cal'ed Heisenberg mordel of ferromagneties are investigate_??_ in detail. The n ain _??_eatures of the results obtained are as follows:-
(1) If the number of nearest neighhours, which shall he designated by _??_ is equal to 2, the result proves to agree exactly with that given by Ising's rigonons treatment of the linear chain problem. since the magnetization vanishes in zero field, this system is not ferromagnetie.
(2) If z_??_3, the existence of the spontaneous magnetization and of the ferromagnetic Curie temperature Tf is predicted. The shape of I-vs.-T ourves for various z values are all nearly alike to that predieted by the Weiss-Heisenberg theory, but are slightly different from it according to their z's.
(3) At temperatures higher than Tf, the curve of the reciprocal of the paramagnetic susceptibility χ is slightly convex toward the T axis. After drawing the asymptote of this 1/χ-vs. T curve, the theoretical paramagnetic Curie temperature T_p may be obtained.
(4) The specific heat anomalies, which originate from the spin configurational energy, are quite similar to those which are predicted by Bethe in his theory regarding the order-disorder transformation of binary alloys.
(5) It is interesting to see the fact that the W.-H. theory of ferro-magnetism is deduced from these results by the same manipulation as that, by which, as was shown in the preceding paper regarding the superlattice problem, the Bragg-Williams theory was deduced from the Bethe theory