Numerical study on spin glass transitions by the non-equilibrium critical relaxation method

Yukiyasu Ozeki, Nobuyasu Ito, 尾関 之康 +1 more

之康 尾関, Yukiyasu Ozeki

Nobuyasu Ito, Takashi Matsuhisa, Hidetsugu Kitatani

The ferromagnetic transition of ± J -Ising spin-glass model on square lattice is studied by using Monte Carlo simulation. At ferromagnetic-bond density p =0.96 where the system shows ferromagnetic transition, the spontaneous magnetization, the ratio < m 4 >/ < m 2 > 2 and the non-equilibrium relaxation (NER) are studied. The transition is estimated to be at K c =0.5100 (1). The analysis by NER gives the most reliable estimation with the least CPU time for simulations among the three methods. The value of magnetization exponent β is estimated to be 0.130(10) which coincides with that of the purely ferromagnetic Ising model ( p =1). The dynamical critical exponent z is estimated to be 2.418(23) from the NER analysis which is different from that of the pure model. The size of simulated lattices is up to 2001×2000, and the number of totally updated Ising spins is 5.5×10 15 .

Nobuyasu Ito, Keita Ogawa, Koji Hukushima +1 more

It is shown that the non-equilibrium relaxation (NER) process of the order-parameter and energy is useful to study the phase transition.By observing the log-derivatives of those decay functions, the critical point is located finely and the critical exponents are estimated accurately.The major advantage of NER method is it's simplicity; not only the behavior in the large-size limit can be observed easily, but also it is not necessary to pursue the equilibrium of the system to get information of the final equilibrium state.Applications are expanding from basic systems like Ising ferromagnets, to spin-glass, quantal system, chiral and KT transitions, and so on.Now the NER process of fluctuations is also expected to share those advantages.It is found that the combinations of the NER functions of some fluctuations provide the way to determine static and dynamics critical exponents directly.

Cheng‐Wei Liu, Anatoli Polkovnikov, Anders W. Sandvik

Nobuyasu Ito, Yukiyasu Ozeki