Conjecture on the low-temperature radius of convergence of the Mayer series

Suppose that $v$ satisfies the stated pair-potential and uniformity assumptions. Let $R^\mathsf{May}(\beta)$ denote the radius of convergence of the Mayer series, and let $e_\infty$ be the ground-state energy per particle. Mayer series' radius-of-convergence conjecture.

$$\lim_{\beta \to \infty} \beta^{-1} \log R^\mathsf{May}(\beta) = e_\infty.$$

This conjecture proposes a physical interpretation of the low-temperature domain of convergence of the Mayer series for attractive potentials. The source states that the only unresolved part is an upper bound on the corresponding limsup.