Analyticity for Locally Stable Hard-Core Gases Via Recursion

Abstract

In their recent works [Comm Math Phys 399:367–388 (2023)] and [Comm Math Phys 406:32 (2025)], Michelen and Perkins proved that the pressure of a system of particles with repulsive pair interactions is analytic for activities in a complex neighborhood of \([0,e\Delta _{\phi }(\beta )^{-1})\), where \(\Delta _{\phi }(\beta )\in (0,C_{\phi }(\beta )]\) denotes what they call the potential-weighted connective constant. This paper extends their method to locally stable (possibly attractive), tempered, and hard-core pair potentials. We obtain an analogous analyticity result that is most effective in the high-temperature regime, where it surpasses the classical Penrose-Ruelle bound of \(C_{\phi }(\beta )^{-1}e^{-(\beta C+1)}\) by at least a factor of \(e^{2}\). The main ingredients in the proof include a recursive identity for the one-point density tailored to locally stable hard-core potentials and a corresponding notion of modulations of an activity function.