The stability of many-body systems

We apply the pair interaction stability criteria of Fisher and Ruelle ( 1966 J. Math. Phys. 7 260) to establish the range of thermodynamic stability for a number of simple analytic potential forms used for condensed matter theory and modelling in the literature. We identify the ranges of potential parameters where, for a given potential, the system is thermodynamically stable, unstable and of uncertain stability. This was further explored by carrying out molecular dynamics simulations on the double Gaussian potential in the stable and unstable regimes. We show that, for example, the widely used exponential-6 and Born-Mayer-Huggins alkali halide potentials produce many-particle systems that are thermodynamically unstable.