Crossing the coexistence line at constant magnetization

Using Monte Carlo histogram methods, the microcanonical caloric curve is computed for the Ising model in two and three dimensions with fixed magnetization. Whereas the signatures of a possible first order phase transition are clearly visible for large systems, intriguing finite size effects are revealed for smaller system sizes. The behaviour of the caloric curve is studied in a systematic way. Furthermore, results for the thermal stability of three-dimensional droplets of minority spins inside the two-phase region are presented. The effect of the percolation transition on the stability of these droplets is discussed.