Study of Hamiltonians with long-range interactions: The XY model

We present a new numerical method to study Hamiltonians with long-range interactions. The CPU time required for the new technique grows like VlnV with the number of degrees of freedom V instead of the $V^2$ dependence naively required. We apply the method to the XY model in 2 and 3 dimensions with a power-law interaction. By studying some critical exponents we show that the short- and long-range models belong to different universality classes.