2D Ising Model Monte Carlo Simulation have some fun and answer the questions. Just Java Monte Carlo Based Simulated Annealing Program . Link to Monte Carlo based functional minimization using analogy to cooling thermodynamic systems, like liquids. 2D Kinetic Monte Carlo Program . A second code is available which is a modification of the first which incorporates ballistic jumps arising, for example, from radiation damage.
Ballistic jumps can wipe out the low-temperature portion of the ordering phase loop.