Magnetization Onsager model

The Ising model has been solved exactly in one and two dimensions Onsager s solution of the model in two dimensions is only at zero field. Infomiation about the Ising model in tliree dunensions comes from high- and low-temperature expansions pioneered by Domb and Sykes [104] and others. We will discuss tire solution to the 1D Ising model in the presence of a magnetic field and the results of the solution to the 2D Ising model at zero field. 

If Onsager s great achievement with the thermodynamics of irreversible processes met with initial indifference, Onsager s next feat created a sensation ill the scientific world. In a discussion remark in 1942, he disclosed that he had solved exactly the two-dimensional Ismg model, a model of a ferro-magnet, and showed that it had a phase transition with a specific heat that rose to infinity at the transi-... 

This condition is similar to that used by Onsager in his own unpublished derivation of the result, Eq. (34), for the spontaneous magnetization of the Ising model. It is to be noted, however, that Devinatz retains conditions (d), (e), and (/). In our theorems, on the contrary, we retain condition (c) but replace (/) by another (slightly stronger) condition on the auxiliary coefficients p and qn defined in Eqs. (29) and (30). To state this we define the monotonically decreasing coefficients... 

The sum in q. III.20 is exactly the same as the partition function for the two-dimensional Ising model of antiferromagnetism in zero magnetic field, which function has been obtained by Onsager (see also Newell and Montroll In terms of the parameter... 

Fig. 11. Temperature dependence of the sublattice magnetization for ErBa2Cu307. The solid curve is the fit to the data of Onsager s exact solution for the 5= 5, 2D Ising model (Lynn et al. 1989).

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