Simulated Tempering and Magnetizing Simulations of the Ising Model

We carried out two-dimensional simulated tempering (ST) simulations of the two-dimensional Ising model with several lattice sizes. We aim to investigate the applicability of the two-dimensional ST to systems with phase transi–tions, and to study crossover of critical scaling behaviors. In the two-dimensional ST simulations, not only temperature but also external field is treated as a dynamical variable. Thus, this method can be referred to as “Simulated Tempering and Magnetizing (STM)”. As has been discussed by previous studies, the ST method is not always compatible with first-order phase transitions. This is also true in the magnetizing process. Processes of flipping the total magnetization hardly occurred during the simulations under Tc in large lattice-size simulations. However, the phase changed through the high temperature region. Therefore, the dimensional extension let us avoid the diffculty of the first-order phase transitions and study a wide area of the phase diagram. We finally study the crossover behavior of the phase transitions with respect to the temperature and external field. The crossover behavior was clearly observed in the simulations in the agreement with the theoretical implications