Abstract
A cell model is introduced in which pairs of particles interact only within the same cell, and then only with a constant couplingφ 0. For positiveφ 0 the statistical thermodynamics is normal, but asφ 0 changes sign, the system manifests a collapse phenomenon with all particles tending to aggregate in the same cell. This collapse instability causes high-temperature series to diverge, but known asymptotic properties of Stirling numbers of the second kind allow one to establish Borel summability. The present model is equivalent to continuum models with bounded pair potentials when in the latter the space dimensionD is permitted to go to 0+.
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