Temperature chaos in 3D Ising spin glasses is driven by rare events

Abstract

-Temperature chaos has often been reported in literature as a rare-event driven phenomenon. However, this fact has always been ignored in the data analysis, thus erasing the signal of the chaotic behavior (still rare in the sizes achieved) and leading to an overall picture of a weak and gradual phenomenon. On the contrary, our analysis relies on a large-deviations functional that allows to discuss the size dependencies. In addition, we had at our disposal unprecedentedly large configurations equilibrated at low temperatures, thanks to the Janus computer. According to our results, when temperature chaos occurs its effects are strong and can be felt even at short distances.Temperature chaos (TC) refers to the complete reorganization of the equilibrium configurations by the slightest change in temperature. This effect was initially predicted in spin glasses (SG) [1][2][3] but it is expected as well in other glassy materials such as polymers [4,5] or vortex glasses [6].An experimental measurement of TC is still missing. The main difficulty arises from the nonequilibrium nature of the experimental glass: since chaos is an equilibrium property, it is not clear how to detect it in nonequilibrium responses (such as the aging magnetic susceptibility [7], for instance). Nevertheless, TC is often regarded as the origin of the anomalous response of glasses in temperature cycles, and in particular, of the spectacular rejuvenation (and memory) effects found in SG [8] (however, see [9,10] for a dissenting view). Although memory and rejuvenation have been also identified in colloids [11], polymers [12,13], ferro-electrics [14,15], and in the ferromagnetic phase of disordered magnetic alloys [16], these are tiny effects as compared to their SG counterpart. Thus, experiments suggest that TC is peculiar in SG.Unfortunately, a rigorous theoretical description of TC has been achieved only for directed polymers in random media in 1+1 dimensions [4,5]. Coming to SG, the analytical work has been mostly concerned with meanfield (MF) approximations. Some accidental cancellations make TC anomalously weak in the SherringtonKirkpatrick model [17] (the standard model in MF approximations), which favored a long controversy about its very existence [18][19][20][21][22][23][24][25]. Only recently the question has been answered in the positive, by the explicit computation of a large-deviation functional (i.e. the free-energy cost of constraining a SG to have similar spin configurations at two temperatures below the critical one, T 1 , T 2 < T c ) [25,26]. A large-deviation functional will play as well a crucial role in this work.Besides, the theoretical work in non MF models is restricted to equilibrium numerical simulations [27][28][29][30][31]. Data were analyzed using a scaling picture (valid for polymers), in which a characteristic length-scale should appear ξ C (T 1 , T 2 ) in the comparison of the system at two temperatures T 1 , T 2 < T c [32,33]. Spin configurations at temperatures T 1 and T 2 would be similar (different), if co...

Glassy dynamics in CuMn thin-film multilayers

“…To quote Ref. 42, "An experimental measurement of TC [temperature chaos] is still missing" (but see Ref. [3] where temperature chaos is reported for a mesoscopic GeMn amorphous spin glass).…”

The three-dimensional Ising spin glass in an external magnetic field: the role of the silent majority

“…The reason is twofold. On one side the number of simulated samples is much smaller than for L < 32, and on the other side temperature chaos, which is stronger the larger the lattice, is probably present [58].…”

Temperature chaos is a non-local effect

“…2 shows, the chaos integral I for a sample has very low correlation to the I value for its APBC transform. Yet, the I's are not normally distributed (because the shape of § For fixed ǫ > 0, T 1 and T 2 the probability of having X T1,T2 > ǫ drops exponentially in L 3 [21,22]. Figure 4.…”

“…3 the most appealing numerical characterization of temperature is the auto-correlation time τ for temperature-mixing along a parallel tempering simulation [22,33]. Unfortunately, a high-accuracy computation of τ is not a light task, so we need an easier-to-compute alternative.…”

“…Unfortunately, τ is very difficult to measure with any precision, even for well equilibrated systems [40]. As shown in [22], see also Appendix B, this difficulty can be skirted by choosing a different quantity, easier to measure but strongly correlated with τ .…”