For a pair potential \(\Phi \) in a general underlying space X satisfying some natural and sufficiently general conditions in the sense of Penrose (J Math Phys 4:1312, 1963) and Poghosyan and Ueltschi (J Math Phys 50:053509, 2009) together with a locally finite measure \(\varrho \) on X we define by means of the so-called Ursell kernel a function r which is shown to be the correlation function of a unique process \(\mathrm{G}\), the limiting Gibbs process for \((\Phi ,\varrho )\) with empty boundary conditions. This process is exhibited as a Gibbs process in the sense of Dobrushin, Lanford and Ruelle for a class of pair potentials, which contains classical stable and hard-core potentials that are called Penrose potentials here. Particularly, a class of positive potentials is included. Finally, for some class of Penrose potentials, we show that \(\mathrm{G}\) is the unique Gibbs process for \(\Phi \). We use the classical method of Kirkwood–Salsburg equations. A decisive role is played by a generalization of Ruelle’s estimate for correlation functions.

对于一般潜在空间X中的一对势\(\Phi \)满足彭罗斯 (J Math Phys 4:1312, 1963) 和 Poghosyan 和 Ueltschi (J Math Phys 50:053509) 意义上的一些自然和充分一般条件， 2009) 连同X上的局部有限测度\(\varrho \)我们通过所谓的 Ursell 核定义了一个函数r，它被证明是一个唯一过程的相关函数\(\mathrm{G}\ )，\((\Phi ,\varrho )\)的极限吉布斯过程有空边界条件。对于一类对势，该过程表现为 Dobrushing、Lanford 和 Ruelle 意义上的 Gibbs 过程，其中包含经典的稳定和硬核势，在此称为 Penrose 势。特别地，包括一类正电位。最后，对于某些类型的彭罗斯势，我们证明\(\mathrm{G}\)是\(\Phi \)的唯一 Gibbs 过程。我们使用 Kirkwood-Salsburg 方程的经典方法。Ruelle 对相关函数的估计的推广起到了决定性的作用。