On the critical slowing down of spin glasses

Vladimir V. Prudnikov, G. B. Teǐtel'Baum

達雄 小森, Hajime Takayama

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, \bar P ( x ) with x = lnτ, is calculated from spin auto-correlation functions simulated. It is found that \bar P ( 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 τ c (= e x c ) is regarded as the critical relaxation time associated with the onset of the spin-glass order at T c , and the branch of \bar P ( 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 \bar P ( 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 ).

I. Riess, Moshe Fibich, A. Ron

Serge Galam, A. Mauger

Postulating homogeneity for the relaxation function, we show that the standard dynamic scaling hypothesis is recovered and that effective relaxation times must decreme upon increasing Kadanoff's blocks sizes. In the case of spin glasses our results are naturally obtained within a diffusion process in the phase space among eigenstates available to the spin system. The model suggests that the critical slowing-down in spin glasses does not result from hierarchically constrained dynamics.

Iveta R. Pimentel

達雄 小森, Hajime Takayama

Slow dynamics in the 'Griffiths phase' of the 3D ± J Ising spin glass is studied by means of Monte Carlo simulation, in which the spectra of (logarithms of) relaxation times, P (x) with x = ln τ, are analyzed in detail. At each temperature P (x) exhibits a characteristic crossover behavior at around a certain value xc which in turn tends to diverge toward the spin-glass critical temperature Tc. The contributions to the branch x ≲ xc are interpreted due to the ordinary critical slowing down process associated with Tc (critical dynamics). The behavior of P (x) at x ≲ xc, on the other hand, is consistent with the picture of relaxation processes of large, rare clusters which are related to the Griffiths singularity at the Curie temperature of the corresponding pure ferromagnet (cluster dynamics).