AbstractThe three‐spin interaction in the form of a box product, σ1× σ2· σ3, is investigated including additional interaction terms in the Hamiltonian in the forms\documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_i {\sigma _{iz},} \sum\limits_{ij} {\sigma _{iz} \sigma _{jz}} $\end{document}, and πiσiz. With the relative strengths considered as parameters, the thermodynamic properties are evaluated as a function of temperature and show considerable variety. Both second‐ and first‐order phase transitio