Temperature and Disorder Chaos in Three-Dimensional Ising Spin Glasses

We study the effects of small temperature as well as disorder perturbations on the equilibrium state of three-dimensional Ising spin glasses via an alternate scaling ansatz. By using Monte Carlo simulations, we show that temperature and disorder perturbations yield chaotic changes in the equilibrium state and that temperature chaos is considerably harder to observe than disorder chaos.

Figure 1

Scaling plot of the chaoticity parameter for temperature chaos (left panel, $T_1=0.20$) and disorder chaos (right panel, $T=0.20$) using $L/{\ell }_c$ as a scaling variable.

Figure 2

Scaling plot of both disorder and temperature chaos. Left: chaoticity parameter $Q$ as a function of $L/{\ell }_c$. Scaling performed with $\zeta =1.16$. Note that ${\ell }_c(\Delta T)\approx A{\ell }_c(\Delta J)$ with $A\approx 8.7$, i.e., disorder chaos appears at considerably shorter length scales than temperature chaos. Right: log-log plot of the same data, plotted as $1-Q$, to illustrate the quality of the scaling.

Figure 3

Distribution of the chaoticity parameter over different realization of the disorder for $L=10$ with $T_1=0.2$ and $T_2=T_1+\Delta T$ [28]. In the case of small $\Delta T$ rare samples have very low values of $Q$ while most of them remain unchanged ($Q=1$). The inset shows a linear-log plot of the data for the smallest values of $\Delta T$ for which $T_1<T_2<2T_c/3$. For all $T_2$ the distribution has a single peak, unlike for the random-energy models with entropic fluctuations [30, 31].