Structure of LowTemperature Phase of a Heisenberg SpinGlass
Project/Area Number 
14540349

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
物性一般(含基礎論)

Research Institution  Tohoku University 
Principal Investigator 
MATSUBARA Fumitaka Tohoku University, Graduate School of Engineering, Professor, 大学院・工学研究科, 教授 (90124627)

CoInvestigator(Kenkyūbuntansha) 
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)

Project Period (FY) 
2002 – 2003

Project Status 
Completed (Fiscal Year 2003)

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)

Keywords  Spinglass / Heisenberg model / MonteCarlo simulation / Genetic algorithm / Parisi state / Replica symmetry Breaking / Nonequilibrium relaxation method / 基底状態 / 低エネルギー励起状態 
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 spinglass 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 spinglass susceptibility diverges at a finite temperature Tc. We have also examined the growth of the spinglass susceptibility on an infinite lattice by mean of a nonequilibrium relaxation simulation and found that the spinglass 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 spinglass phase. 2.Nature of the spinglass phase We have developed a powerfull genetic algorithm for searching for the ground state and metastable states of a Heisenberg spinglass model. Using the algorithm, we have examined the ground state and lowlying 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 lowlying 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 spinglass phase of the Heisenberg model is well described by a replicasymmetrybreaking theory which was proposed in the infiniterange spinglass model.

Report
(3 results)
Research Products
(16 results)