In their recent works [Comm. Math. Phys. 399:1 (2023)] and [arXiv:2109.01094], Michelen and Perkins proved that the pressure of a system of particles with repulsive pair interactions is analytic for activities up to $e\Delta_{ \phi}(\beta)^{ -1}$, where $\Delta_{ \phi}(\beta)\in(0,C_{ \phi}(\beta)]$ is a constant they called the potential-weighted connective constant. This paper extends their method to locally stable, tempered, and hard-core pair potentials. Our main result is that the pressure of such a system is analytic for activities up to $e^{ 2-2W(eA_{ \phi}(\beta)/\Delta_{ \phi}(\beta))}\Delta_{ \phi}(\beta)^{ -1}e^{ -(\beta C+1)}$, where $C\ge0$ is the local stability constant, $W(\cdot)$ the Lambert $W$-function, $A_{ \phi}(\beta)$ the contribution from the attraction in the pair potential to the temperedness constant, and $\Delta_{ \phi}(\beta)\in[A_{ \phi}(\beta),C_{ \phi}(\beta)]$ a counterpart of the constant defined by Michelen and Perkins. 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. In the high-temperature regime, our result surpasses the classical Penrose-Ruelle bound of $C_{ \phi}(\beta)^{ -1}e^{ -(\beta C+1)}$ by at least a factor of $e^{ 2}$.
Categories: math-ph cond-mat.stat-mech math.MP math.PR