We study the Lee-Yang polynomials arising from the partition function of the Curie-Weiss model throught their relation to the unitary Hermite polynomials $H_{n}\left(z ; \sigma^{2} / n\right)$. Using saddle-point analysis of their integral representations, we develop a unified asymptotic theory for $H_{n}\left(z ; \sigma^{2} / n\right)$. We show that the zeros lie on an arc of the unit circle when σ<2, fill the entire circle when σ>2, and display an Pearcey-type universal behavior near the critical value σ=2. These results deepen the Lee-Yang theory for the Curie-Weiss model and provide new analytic tools for the asymptotic analysis of Lee-Yang polynomials.
LI Shuhai
,
HU Tiening
,
WANG Dong
. Plancherel-Rotach asymptotics of unitary Hermite polynomials and distribution of Lee-Yang zeros of Curie-Weiss model*[J]. Journal of University of Chinese Academy of Sciences, 0
: 29
.
DOI: 10.7523/j.ucas.2026.018
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