Collapsing systems

The stability problem posed in statistical mechanics by self-gravitating systems is discussed for the simpler case of systems with a purely attractive nonsingular pair potential of short range. Molecular-dynamics simulations of such systems are reported and are found to agree remarkably well with a modified version of the Hertel-Thirring cell model. A first-order phase transition is observed between a homogeneous phase at high energies and a collapsing phase with a single, very compact cluster in a diluted homogeneous background at low energies. The latter is not an extensive or thermodynamic phase. According to the cell model, really large systems are most likely to be found in a critical state hesitating between these two phases.