Dynamical temperature study for classical planar spin systems

Making use of the Rugh's micro-canonical approach to temperature we study XY-spin systems by the strictly energy conserving over-relaxation algorithm. In this micro-canonical simulation the temperature and also the specific heat are determined as averages of expressions easy to implement. The XY-chain is studied for a test. The second order transition on a cubic lattice and the first order transition on fcc lattice are analyzed in greater detail to have a more severe test about the feasibility of this micro-canonical method.