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تسجيل مستخدم جديدSimulated Tempering and Magnetizing: An Application of Two-Dimensional Simulated Tempering to Two-Dimensional Ising Model and Its Crossover
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We performed two-dimensional simulated tempering (ST) simulations of the two-dimensional Ising model with different lattice sizes in order to investigate the two-dimensional STs applicability to dealing with phase transitions and to study the crossover of critical scaling behavior. The external field, as well as the temperature, was treated as a dynamical variable updated during the simulations. Thus, this simulation can be referred to as Simulated Tempering and Magnetizing (STM). We also performed the Simulated Magnetizing (SM) simulations, in which the external field was considered as a dynamical variable and temperature was not. 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. Flipping of the entire magnetization did not occur in the SM simulations under $T_mathrm{c}$ in large lattice-size simulations. However, the phase changed through the high temperature region in the STM simulations. Thus, the dimensional extension let us eliminate the difficulty of the first-order phase transitions and study wide area of the phase space. We then discuss how frequently parameter-updating attempts should be made for optimal convergence. The results favor frequent attempts. 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 agreement with the theoretical implications.
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We applied the simulated tempering and magnetizing (STM) method to the two-dimensional three-state Potts model in an external magnetic field in order to perform further investigations of the STMs applicability. The temperature as well as the external
field are treated as dynamical variables updated during the STM simulations. After we obtained adequate information for several lattice sizes $L$ (up to $160times 160$), we also performed a number of conventional canonical simulations of large lattices, especially in order to illustrate the crossover behavior of the Potts model in external field with increasing $L$. The temperature and external field for larger lattice size simulations were chosen by extrapolation of the detail information obtained by STM. We carefully analyzed the crossover scaling at the phase transitions with respect to the lattice size as well as the temperature and external field. The crossover behavior is clearly observed in the simulations in agreement with theoretical predictions.
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