Application of cellular automata to N-body systems

A two-dimensional cellular automaton model is introduced to deal with the dynamics of a finite system of particles whose interactions are simulated by two-body step potentials. The method is illustrated for a potential approximating the standard Lennard-Jones potential, representative for the problem of heavy ion collisions in nuclear physics. From the cellular automaton dynamics thermodynamic equilibrium state variables are introduced in the usual way. The numerical experiments indicate the occurrence of a phase transition. Macroscopically the transition is marked by a singularity in the equation of state; microscopically it manifests itself by the formation of clusters of particles of all sizes, obeying a mass distribution in the form of a power law of exponent 1.35.