Ising model properties

To obtain a clearer insight into the relationship between the Ising and self-avoiding walk enumerations, it is better to pass to the logarithm of the partition function, In Z, since this eliminates the need to consider disjoint graphs. We can then find a property of the Ising model which corresponds to each of C , u , (R 2), f (x) dx. The Ising enumerations are much more... 

The most effective reply to this criticism is a reference to the two-dimensional Ising model for which an analytic solution is available, and coefficients can be computed for all values of n. Taking the triangular lattice, for example, predictions based on values of n up to 15 are quite adequate to represent the asymptotic behavior of the coefficients relating to thermodynamic and correlation properties to a high degree of accuracy. 

Two ions are well-known for their highly anisotropic properties. Firstly, in the rare-earth family, Dy3+ which has a 6H15/2 ground state. The spin-orbit interaction is stronger than the crystal field effects. The ratio J /J can be of the order of 100 (Jj. = 0), gjj = 20 and gi = 0 this is practically an ideal case. Secondly, in the transition element series, the ion Co2+ is also characterized by anisotropic interactions (either in the tetrahedral or octahedral coordination), the anisotropy being however lower than in the case of Dy3+. J /J is about 0.5 for this ion. Some Fe2+ compounds also display a behavior approximating to the Ising model. 

III. C of two different properties of the ID Ising model, namely, its average squared magnetization and its partition function. 

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