Next-Nearest-Neighbor Ising Model

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Abstract
The next‐nearest‐neighbor two‐dimensional Ising model is cast into a form which resembles a one‐dimensional interacting many‐fermion system. An approximation, which has previously been shown to be successful in giving the critical properties of the two‐dimensional ferroelectric problem, is used. From the approximate expression obtained, the critical indices are found to be α = α′ = 0, β = ⅛, which agrees with the results obtained from series expansions and plausible physical arguments. The critical temperature obtained agrees to within 6% of the series expansion results.

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