Monte Carlo Simulations Of Mixed Spin Ising Model

As a mathematical model of ferromagnetism in statistical mechanics, the Ising model has received much attention. Considering the ferrimagnetics, there are much more works to mixed spin Ising model which assumed the two particles with different spin. D.S. Cambui et al. studied the system of different concentration on square lattice by Monte Carlo simulations in2012. Because of the massive calculation, the precision of the results is lower than pure Ising model’s. Owing to GPU’s powerful calculation capability, heterogeneous algorithm on GPU and CPU were used widely. In this work, we aimed at observing the critical behavior of mixed spin Ising model. Based on Monte Carlo method on GPU, we simulated the mixed spin (spin-1and spin-1/2) Ising model on triangular and square lattice. The lattice sizes range from16to1024. Considering the periodic boundary, nearest-neighbor interaction and nine different concentration of spin-1/2, we got more accurate critical temperature than Cambui’s on square lattice with less computing time. With this technology, results were obtained up to40times faster on the GPU than on a current CPU on a1024*1024triangular lattice. During the simulation, the physical quantity containing the magnetization, the susceptibility, the specific heat and Binder cumulant were measured. The critical temperature (β) and exponents (yt, yh) were gained through fitting the Binder cumulant and susceptibility for different concentration. We also inferred the relationship between critical temperature and concentration:β=A1*exp(-X/l1)+y0.