Critical dynamics and cluster dynamics of the 3D+/-J ising spin-glass model in its 'Griffiths phase'

Non-exponential slow dynamics in the 'Griffiths phase' of the three-dimensional (3D) +/-J Ising spin-glass model is studied by means of Monte Carlo simulation. The distribution of relaxation times averaged over samples, (P) over bar(x) with x = ln tau, is calculated from spin auto-correlation functions simulated. It is found that (P) over bar(x) consists of two branches. The cross-over value between the branches, x(c), diverges as T --> T-c, T-c being the spin-glass transition temperature. Therefore tau(c) (= e(xc)) is regarded as the critical relaxation time associated with the onset of the spin-glass order at T-c, and the branch of (P) over bar(x) at x < x(c) is interpreted due to the ordinary critical slowing down process (critical dynamics). The other branch at x > x(c) causes the unusual slow dynamics peculiar to spin glasses. Various aspects of (P) over bar(x) of this branch examined are consistent with the following picture; compact regions with less frustrations than the system as a whole are thermally fluctuating with very small frequencies, and independently of each others (cluster dynamics).