
The model of ferromagnetism proposed by Ising is treated by synthesizing a cluster treatment with the spherical model. The spherical model is used to determine approximately the molecular field acting on the cluster and the effective interactions between dipoles of the cluster.The method is applied to the square net and to the cubic lattice and the critical temperatures are obtained. The result for the square net is that $\frac{E}{k{T}_{c}}=0.831$ and for the cubic lattice that $\frac{E}{k{T}_{c}}=0.442$. In these results $E$ is the energy required to change an adjacent pair of dipoles from parallel to antiparallel relative orientation.
mechanics of solids
mechanics of solids
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