Theoretical Investigations on the spin-glass phase transitions and its low-temperature phase using the nonequilibrium relaxation method

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The aim of this research project is to clarify the spin-glass (SG) transition in the Heisenberg spin-glass model in three dimensions. In order to achieve thorough understandings of the SG transition and the low-temperature phase, we also investigated the XY model and the Ising model. Our main results are as follows.1.Development of efficient numerical recipes : We developed various protocols of the finite-time scaling analysis in order to improve the accuracy.2.Resolution of the spin- and the chiral-glass transitions in the Heisenberg SG model in three dimensions : The chiral-glass transition is confirmed to occur at higher temperature than the spin-glass transition temperature. We also observed that the spin and the chirality are decoupled above the SG transition temperature and become coupled below it.3.Dynamic universality : We found a possibility of the dynamic universality in the spin- and the chiral-glass transitions in three dimensions. All the investigated phase transition exhibit the same dynamic critical exponent.4.Low-temperature crossover in the SG phase : We found a crossover temperature in the spin-glass phase, where the ground-state relaxation appears. The dynamic behavior below this crossover temperature is equivalent to the T=0 dynamics. A dynamic exponent of the ground state is also estimated. It takes almost the same value between the Ising model and the Heisenberg model.5.Preparation for the quantum spin-glass problems : We investigated the quantum phase transition of the random alternating quantum spin chain. Our developed method is confirmed to be applicable to this interesting problems.