Short-range type critical behavior in spite of long-range interactions: the phase transition of a Coulomb system on a lattice

One- to three-dimensional hypercubic lattices half-filled with localized particles interacting via the long-range Coulomb potential are investigated numerically. The temperature dependences of specific heat, mean staggered occupation, and of a generalized susceptibility indicate order-disorder phase transitions in two- and three-dimensional systems. The critical properties, clarified by finite-size scaling analysis, are consistent with those of the Ising model with short-range interaction.