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A variational approximation to the Ising model in a magnetic field (T<~T₂), based on the zero-field solution, yields an upper bound on the free energy, an approximate equation of state, and a lower bound on the magnetization, all having the correct critical indices. In two dimensions, these are numerically evaluated, and compared with the results of series expansions.
Krinsky et al. (Mon,) studied this question.
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