Monte Carlo simulations are performed for the spin- XY model in two dimensions for large (up to 24×24 sites) lattices. Results are obtained over a wide temperature range which includes the critical temperature Tc, estimated to be 0.4-0.5. The energy, specific heat, vortex density, and derivative of the helicity modulus are given as functions of temperature. As the lattice size is increased, the specific heat per spin approaches a finite value and does not diverge. © 1985 The American Physical Society.