Statistical mechanics of a two-dimensional system with long-range interactions

We analyse the statistical physics of a two-dimensional lattice-based system with long-range interactions. The particles interact in a way analogous to the queens on a chess board. The long-range nature of the interaction gives the mathematics of the problem a simple geometric structure which simplifies both the analytic and numerical study of the system. We present some analytic calculations for the statics of the problem and we also perform Monte Carlo simulations which exhibit a dynamical transition between a high-temperature liquid regime and a low-temperature glassy regime exhibiting ageing in the two time-correlation functions.