Lee-Yang Zeros And Particle Fluctuations
Mohamed El Hedi Bahri, Ian Jauslin, Joel L. Lebowitz
2026
Abstract
We consider classical particles in the continuum in the grand canonical ensemble, with a stable, tempered and lower-regular pair potential and boundary conditions of uniformly bounded density. We prove that if the Lee-Yang zeros of the grand canonical partition function in the complex fugacity plane =e^{betamu}$ remain bounded away from a real point >0$ for all sufficiently large volumes, then along cubes the thermodynamic limit and differentiation commute at $: every derivative of the finite-volume pressure in the chemical potential converges, uniformly in a neighborhood of $, to the corresponding derivative of the limiting pressure. The limiting values of all derivatives are independent of the boundary condition; in particular, the density and the particle-number variance per unit volume converge to $beta^{-1}partial_mu p$ and $beta^{-2}partial^2_mu p$, respectively. The result extends to the unbounded boundary conditions of Procacci and Yuhjtman for super-stable potentials in addition to Ruelle's tempered boundary conditions.
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- arXiv preprint: arXiv:2607.26975.