Monte Carlo Simulations of Doped, Diluted Magnetic Semiconductors - a System with Two Length Scales

We describe a Monte Carlo simulation study of the magnetic phase diagram of diluted magnetic semiconductors doped with shallow impurities in the low concentration regime. We show that because of a wide distribution of interaction strengths, the system exhibits strong quantum effects in the magnetically ordered phase. A discrete spin model, found to closely approximate the quantum system, shows long relaxation times, and the need for specialized cluster algorithms for updating spin configurations. Results for a representative system are presented.Comment: 12 pages, latex, 7 figures; submitted to International Journal of Modern Physics C, Proceedings of the U.S.-Japan Bilateral Seminar: Understanding and Conquering Long Time Scales in Computer Simulation