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We applied the simulated tempering and magnetizing (STM) method to thetwo-dimensional three-state Potts model in an external magnetic field in orderto perform further investigations of the STM's applicability. The temperatureas well as the external field are treated as dynamical variables updated duringthe STM simulations. After we obtained adequate information for several latticesizes $L$ (up to $160\times 160$), we also performed a number of conventionalcanonical simulations of large lattices, especially in order to illustrate thecrossover behavior of the Potts model in external field with increasing $L$.The temperature and external field for larger lattice size simulations werechosen by extrapolation of the detail information obtained by STM. We carefullyanalyzed the crossover scaling at the phase transitions with respect to thelattice size as well as the temperature and external field. The crossoverbehavior is clearly observed in the simulations in agreement with theoreticalpredictions.

Application of Simulated Tempering and Magnetizing to a Two-Dimensional Potts Model