= Blume–Emery–Griffiths model
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The classical Blume–Emery–Griffiths model uses spins $\sigma_i\in\{-1,0,1\}$ with both bilinear $\sigma_i\sigma_j$ and biquadratic $\sigma_i^2\sigma_j^2$ nearest-neighbour interactions, together with a single-site term proportional to $\sigma_i^2$. One convention is $H=-J\sum\sigma_i\sigma_j-L\sum\sigma_i^2\sigma_j^2-D\sum\sigma_i^2-h\sum\sigma_i$. Signs of the single-site parameter vary across conventions. Setting $L=0$ gives a <Blume–Capel model> after matching that sign convention. The one-dimensional version admits an exact <spin-chain transfer matrix>.
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