| Project/Area Number |
14540349
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
物性一般(含基礎論)
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| Research Institution | Tohoku University |
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Principal Investigator |
MATSUBARA Fumitaka Tohoku University, Graduate School of Engineering, Professor, 大学院・工学研究科, 教授 (90124627)
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| Co-Investigator(Kenkyū-buntansha) |
SHIRAKURA Takayuki Iwate University, Humanity and Social Science, Professor, 人文社会科学部, 教授 (90187534)
NAKAMURA Tohta Tohoku University, Graduate School of Engineering, Research Associate, 大学院・工学研究科, 助手 (50280871)
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| Project Period (FY) |
2002 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2002: ¥2,000,000 (Direct Cost: ¥2,000,000)
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| Keywords | Spin-glass / Heisenberg model / Monte-Carlo simulation / Genetic algorithm / Parisi state / Replica symmetry Breaking / Non-equilibrium relaxation method / 基底状態 / 低エネルギー励起状態 |
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| Research Abstract |
1.Phase transition of the +/-J Heisenberg spin glass model
We have investigate the phase transition of the +/-J Heisenberg model by means of two Monte Carlo simulations. In the equilibrium simulation, we have calculated a spin-glass susceptibility for various sizes of the lattice and extrapolated it to that for an infinite lattice using a finite size scaling analysis. The result has suggested that the spin-glass susceptibility diverges at a finite temperature Tc. We have also examined the growth of the spin-glass susceptibility on an infinite lattice by mean of a non-equilibrium relaxation simulation and found that the spin-glass susceptibility exhibits a critical behavior at the same temperature Tc. Thus we conclude that a phase transition occurs in the +/-J Heisenberg model and the low temperature phase of the model is a spin-glass phase.
2.Nature of the spin-glass phase
We have developed a powerfull genetic algorithm for searching for the ground state and metastable states of a Heisenberg spin-glass model. Using the algorithm, we have examined the ground state and low-lying metastable states of the model on various sizes of the lattice and found that Parisi states are realized in the model. That is, there are many low-lying metastable states whose energies are almost the same as the ground state energy and which are separated from the ground state by an infinitely large energy barrier. We have also examined excitations near the Prisistates and found that those excitations have properties similar to those of the pure ferromagnetic model. On the basis of those results, we have suggested that the spin-glass phase of the Heisenberg model is well described by a replica-symmetry-breaking theory which was proposed in the infinite-range spin-glass model.
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