โ Scribed by R.G. Bowers
No coin nor oath required. For personal study only.
The Curie-Weiss Ising model is refined so that repeated finite clusters of nearest-neighbour interactions can be considered. The spins in the boundaries of these clusters interact via the usual artificially long-ranged interactions. The model is solved exactly for any basic cluster although explicit results are given in only a few cases. It is shown that, for any choice of cluster, the basic thermodynamic properties of the model are identical with those of some related effective field approximation. The connection between such approximations and standard cluster approximation schemes is discussed at some length. In the cases of a single spin and of an interacting spin pair, the related approximations are the mean-field and Oguchi approximations, respectively. Attention is focused on the Curie point and associated critical phenomena. Many standard critical exponents are calculated exactly. Classical exponent values result for all clusters.
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