Lennard-Jones气体的Mayer级数：收敛半径的改进界
The Mayer series of the Lennard-Jones gas: improved bounds for the convergence radius
摘要：
本文给出了Lennard-Jones气体的Mayer级数的收敛半径的一个下界，它大大改进了Penrose和Ruelle在1963年得到的经典界。为了获得这个结果，我们使用了Morais等人最近提出的另一种估计（J. Stat. Phys.2014）对于受限类别的稳定和回火对势（即，可以被写为非负势加上绝对可积和稳定势的总和的那些），结合由Locatelli和Schoen（J. Glob. Optim。2002年）建立了一个下界的粒子之间的最小原子间的距离通过一个莫尔斯势相互作用在一个集群的最小能量配置。
英文摘要：
We provide a lower bound for the convergence radius of the Mayer series of the Lennard-Jones gas which strongly improves on the classical bound obtained by Penrose and Ruelle 1963. To obtain this result we use an alternative estimate recently proposed by Morais et al. (J. Stat. Phys. 2014) for a restricted class of stable and tempered pair potentials (namely those which can be written as the sum of a non-negative potential plus an absolutely integrable and stable potential) combined with a method developed by Locatelli and Schoen (J. Glob. Optim. 2002) for establishing a lower bound for the minimal interatomic distance between particles interacting via a Morse potential in a cluster of minimum-energy configurations.
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