Spin correlations between neighboring sites

Finally it is of interest to compute spin correlations between neighboring sites, i.e. 

Consider a. plane square lattice Ising model with a spin variable s J = 1 associated with the site (i,j) and interactions between nearest-neighbor sites. Kaufman and Onsager3 4 have shown how the spin-spin correlation functions in an infinite lattice,... 

Here Tc is the dipolar correlation time, Av is the observed linewidth, and Avq is the rigid lattice linewidth measured at a temperature low enough that diffusion effects are no longer detectable. For Aptemperature dependence of Ap and Tc is normally set equal to the atomic jump time on the grounds that an atomic jump from one site to another alters the dipolar interaction between neighboring spins substantially. Since the atomic jump frequency is expected to obey an Arrhenius relation [Zener (1952)], Tc should also show such a dependence on temperature. The n values obtained from line-narrowing measurements have usually been fit to the relation... 

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