We demonstrate a quasipolynomial-time deterministic approximation algorithm for the partition function of a Gibbs point process interacting via a finite-range stable potential. This result holds for all activities $\lambda$ for which the partition function satisfies a zero-free assumption in a neighborhood of the interval $[0,\lambda]$. As a corollary, for all finite-range stable potentials we obtain a quasipolynomial-time determinsitic algorithm for all $\lambda < /(e^{B + 1} \hat C_\phi)$ where $\hat C_\phi$ is a temperedness parameter and $B$ is the stability constant of $\phi$. In the special case of a repulsive potential such as the hard-sphere gas we improve the range of activity by a factor of at least $e^2$ and obtain a quasipolynomial-time deterministic approximation algorithm for all $\lambda < e/\Delta_\phi$, where $\Delta_\phi$ is the potential-weighted connective constant of the potential $\phi$. Our algorithm approximates coefficients of the cluster expansion of the partition function and uses the interpolation method of Barvinok to extend this approximation throughout the zero-free region.

翻译：我们为具有有限范围稳定势相互作用的吉布斯点过程的配分函数，提出了一种拟多项式时间确定性近似算法。该结果适用于所有满足零自由假设的活性$\lambda$（该假设在区间$[0,\lambda]$的邻域内成立）。作为推论，针对所有有限范围稳定势，我们得到了当$\lambda < /(e^{B + 1} \hat C_\phi)$时的拟多项式时间确定性算法，其中$\hat C_\phi$为有界性参数，$B$为势函数$\phi$的稳定性常数。对于排斥势（如硬球气体）的特殊情形，我们将活性范围至少改进了$e^2$倍，并获得了当$\lambda < e/\Delta_\phi$时的拟多项式时间确定性近似算法，其中$\Delta_\phi$为势函数$\phi$的势加权连接常数。我们的算法通过近似配分函数簇展开系数，并利用Barvinok插值方法将这一近似扩展至整个无零区域。