The Lee-Yang property of the Blume-Capel model

Abstract

The Lee-Yang theory is based on the theorem concerning a property of the ferromagnetic Ising model partition function proved by T. D. Lee and C. N. Yang in 1952. It provides powerful tools for understanding the very nature of phase transitions and critical phenomena in various spin and similar models. Sometimes, this theory is applied to models for which the theorem's validity has not been proved. By the main result of E. H. Lieb and A. D. Sokal, Commun. Math. Phys. 80, 153 (1981), for a given ferromagnetic model, this validity is guaranteed by the same property of the single-spin partition function. Due to the anisotropy term $\sum_i ΔS_i^2$, the single-spin partition function of the Blume-Capel model fails to have the Lee-Yang property for $βΔ> \ln 2$. In this article, we show that the ferromagnetic interaction in such a model can induce the Lee-Yang property, even for these values of $βΔ$. To the best of our knowledge, it is the first result of this kind.