Cluster Heat Bath Monte Carlo Method of Complicated Spin Systems
Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants|
|Research Institution||IWATE UNIVERSITY|
SHIRAKARA Takayuki Iwate University, Department of humanities and Social Sciences, Associate Professor, 人文社会科学部, 助教授 (90187534)
MATSUBARA Fumitaka Tohoku University, Department of Applied Physics, Professor, 工学部, 教授 (90124627)
SHINDO Koichi Iwate University, Department of humanities and Social Sciences, Professor, 人文社会科学部, 教授 (10004384)
|Project Period (FY)
1998 – 1999
Completed(Fiscal Year 1999)
|Budget Amount *help
¥2,300,000 (Direct Cost : ¥2,300,000)
Fiscal Year 1999 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1998 : ¥1,400,000 (Direct Cost : ¥1,400,000)
|Keywords||spin glass / Monte Carlo Method / Random spin system / effective algorithm / Complicated spin system / Neasal Network / ANNNI model / frustsation / モンテカルロシミュレーション|
The cluster heat bath (CHB) method, which was devised in the study of quasi-one dimensional spin systems, can also become an effective method for complicated spin systems with frustrations. Then in this research, the CHB method has been applied for spin glass models and the ANNNI model, and the following results have been obtained.
1. Ising spin glasses (SG) in two dimensions
In this case we have obtained numerical results that show a SG transition at a finite temperature in the 【plus-minus】J model and at zero temperature in the Gaussian model. Clear differences between these two models have been observed in the following quantities; (1) the size dependence of defect free energies at low temperatures, (2) the size dependence of the Binder parameter of spin freezing and (3) the finite size scaling of physical quantities.
2. Heisenberg spin glasses in two and three dimensions
It has been believed for the Heisenberg SG that the SG phase is not realized at finite temperatures even in three dim
ensions. One of the evidences is a decrease of the defect energy with an increase of the system size. We have seen from the study of the Ising SG, however, that values of the defect energy strongly depend on its definition. Here we have investigated an increase of the energy when the ground state is twisted around some axis, which is supposed to be a natural definition of the defect energy in the Heisenberg model. Stiffness exponents obtained in this method are much larger than the previous values, but rather similar to those of the pure ferromagnetic models.
3. The ANNNI model in two dimensions
In this model, though it was shown that there are two transition temperatures the values and properties of those were not obvious, due to the difficulty of the numerical methods. By means of the CHB method, it has been shown that the transitions at high and low temperatures belong to the Kosterlitz-Thouless type and the Pokrovsky-Talapov type, respectively.
4. Neural networks for the associate memory
We have applied a learning-unlearning process to the Hopfield model with hierarchically structured information, and showed that large improvements of the memory capacity and so on are realized. Less
Research Products (14results)