AC susceptibilities and relaxation time distributions for the two-dimensional and three-dimensional +or-J Ising spin glasses

Abstract

By means of two different methods in a Monte Carlo simulation, the authors calculate the AC susceptibilities chi ( omega ) and relaxation time distributions g( tau ) in the +or-J Ising two-dimensional (2D) and three-dimensional (3D) spin glasses. The data obtained by the two methods separately are confirmed to be consistent with each other through the fluctuation dissipation theorem chi ( omega )=(1/T) integral d tau g( tau )/(1-i omega tau ). The imaginary parts Im chi of the AC susceptibilities show a characteristic difference in the 2D and 3D spin glasses; as the frequency of the AC field is decreased, the height of the peak of Im chi becomes higher in the 2D spin glass, and lower in the 3D spin glass. They can also see a difference between the g( tau ) distributions in the 2D and 3D spin glasses, reflected by the difference in the chi ( omega )-values. In the 3D spin glass, Im chi has no frequency dependence at low temperatures, suggesting that the fluctuation spectrum of the magnetization shows 1/f-noise behaviour in the spin-glass phase.