The partition functions of generalised Ising-type models on the square lattice can be approximated in terms of the partition functions for finite n*n, n*(n-1) and (n-1)*(n-1) lattices. When expressed as high-temperature series, these approximations give terms through to order 2n or 2n+1 correctly.
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Enting et al. (1977) studied this question.
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