Abstract
Using an extended Lee-Yang theorem and GKS correlation inequalities, we prove, for a class of ferromagnetic multi-spin interactions, that they will have a phase transition (and spontaneous magnetization) if, and only if, the external field h = 0 (and the temperature is low enough). We also show the absence of phase transitions for some nonferromagnetic interactions. The FKG inequalities are shown to hold for a larger class of multi-spin interactions.
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Communicated by H. Spohn
In memory of Julius Borcea
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Lebowitz, J.L., Ruelle, D. Phase Transitions with Four-Spin Interactions. Commun. Math. Phys. 304, 711–722 (2011). https://doi.org/10.1007/s00220-011-1250-9
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DOI: https://doi.org/10.1007/s00220-011-1250-9