Optimized energy calculation in lattice systems with long-range interactions

We discuss an efficient approach to the calculation of the internal energy in numerical simulations of spin systems with long-range interactions. Alth ough, since the introduction of the Luijten-Blote algorithm, Monte Carlo si mulations of these systems no longer pose a fundamental problem, the energy calculation is still an O(N-2) problem for systems of size N. We show how this can be reduced to an O(N logN) problem, with a break-even point that i s already reached for very small systems. This allows the study of a variet y of, until now hardly accessible, physical aspects of these systems. In pa rticular, we combine the optimized energy calculation with histogram interp olation methods to investigate the specific heat of the Ising model and the first-order regime of the three-state Ports model with long-range interact ions.