Journal of Statistical Physics, Vol. 23, No. 2, 1980, p. 219-230.
A cell model is introduced in which pairs of particles interact only within the same
cell, and then only with a constant coupling ~b 0 . For positive q5 o the statistical
thermodynamics is normal, but as q50 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 dimension D is permitted to go to 0 +.