Rigorous results on the triangular Ising model with pair and triplet interactions

Abstract It is shown that the Ising model on the triangular lattice with pair and triplet spin interactions and an external magnetic field is completely equivalent to an Ising model on the diced lattice with only nearest neighbor interactions and a staggered magnetic field. The Yang-Lee zero consideration is then used to determine regimes in the parameter space of the triangular Ising model that are free of phase transitions.

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