On the Lee-Yang property of some ferromagnets

2025/03/05 by Kozitsky, Yuri
#30D15 #82B20 #82B27 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2503.03510

Abstract

According to the Lieb-Sokal theorem, the partition function, Z, of a ferromagnetic spin model has the Lee-Yang property if the single-spin partition function has it. In this note, it is shown that for some spin models a ferromagnetic interaction can induce the Lee-Yang property of Z even if the single-spin partition function fails to have it. In particular, this holds for the Blume-Capel model and for the annealed states of the s=± 1 site dilute Ising model with a neares-neighbor interaction on \mathdsZ^d, as well as with interactions defined by a hierarchical structure similar to that of Dyson's hierarchical model.

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