We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to L = 40 using the Janus dedicated computer. Our analysis takes into account leading-order corrections to scaling. We obtain T c = 1.1019(29) for the critical temperature, ν = 2.562(42) for the thermal exponent, η = −0.3900(36) for the anomalous dimension, and ω = 1.12(10) for the exponent of the leading corrections to scaling. Standard (hyper)scaling relations yield α = −5.69(13), β = 0.782(10), and γ = 6.13(11). We also compute several universal quantities at T c .

Experiments on spin glasses can now make precise measurements of the exponent z(T) governing the growth of glassy domains, while our computational capabilities allow us to make quantitative predictions for experimental scales. However, experimental and numerical values for z(T) have differed. We use new simulations on the Janus II computer to resolve this discrepancy, finding a time-dependent z(T,t_{w}), which leads to the experimental value through mild extrapolations. Furthermore, theoretical insight is gained by studying a crossover between the T=T_{c} and T=0 fixed points.

We first reproduce on the Janus and Janus II computers a milestone experiment that measures the spinglass coherence length through the lowering of free-energy barriers induced by the Zeeman effect. Secondly, we determine the scaling behavior that allows a quantitative analysis of a new experiment reported in the companion Letter [S. Guchhait and R. Orbach, Phys. Rev. Lett. 118, 157203 (2017)]. The value of the coherence length estimated through the analysis of microscopic correlation functions turns out to be quantitatively consistent with its measurement through macroscopic response functions. Further, nonlinear susceptibilities, recently measured in glass-forming liquids, scale as powers of the same microscopic length.

Spin glasses are a longstanding model for the sluggish dynamics that appear at the glass transition. However, spin glasses differ from structural glasses in a crucial feature: they enjoy a time reversal symmetry. This symmetry can be broken by applying an external magnetic field, but embarrassingly little is known about the critical behavior of a spin glass in a field. In this context, the space dimension is crucial. Simulations are easier to interpret in a large number of dimensions, but one must work below the upper critical dimension (i.e., in d < 6) in order for results to have relevance for experiments. Here we show conclusive evidence for the presence of a phase transition in a four-dimensional spin glass in a field. Two ingredients were crucial for this achievement: massive numerical simulations were carried out on the Janus special-purpose computer, and a new and powerful finite-size scaling method. T he glass transition differs from standard phase transitions in that the equilibration time of glass formers (supercooled liquids, polymers, proteins, superconductors, etc.) diverges without dramatic changes in their structural properties (1-3). The reconciliation of the dynamic slowdown with the apparent immutability of glass formers is a major challenge for condensed matter physics.Spin glasses [which are disordered magnetic alloys (4)] enjoy a privileged status in this context, as they provide the simplest model system both for theoretical and experimental studies of a glassy dynamics. On the experimental side, time-dependent magnetic fields provide a wonderful tool to probe the dynamic response, which can be accurately measured with a SQUID (for instance, see ref. 5). On the theoretical side, magnetic systems are notably easier to model and to simulate numerically. In fact, special-purpose computers have been built for the simulation of spin glasses (6-9).Yet, spin glasses differ from most glassy systems in a crucial feature: like all magnetic systems, they enjoy time-reversal symmetry in the absence of an applied magnetic field. In fact, we now know that their glassy dynamics are due to a bona fide phase transition in which the time-reversal symmetry is spontaneously broken (10-12). Yet, in the presence of an applied magnetic field, the experimental spin-glass dynamics is just as glassy, although the field explicitly breaks the symmetry.However, whether spin glasses in a magnetic field undergo a phase transition has been a long-debated and still open question (see refs. 13, 14 for recent, opposed views). In the mean-field approximation, which is valid for large spatial dimension down to the upper critical dimension d u ¼ 6 (15), the de AlmeidaThouless line separates the high-temperature paramagnetic phase from the glassy phase (16)*. Yet, recent numerical simulations in spatial dimensions below d u did not find the transition in a field (18,19). Experimental studies have been conducted as well, with conflicting conclusions (20-23). In spite of these difficulties, it has been argued that the would-be spi...

Abstract. We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L = 32 lattices down to T ≈ 0.64T c . We demonstrate the relevance of equilibrium finite-size simulations to understand experimental non-equilibrium spin glasses in the thermodynamical limit by establishing a time-length dictionary. We conclude that non-equilibrium experiments performed on a time scale of one hour can be matched with equilibrium results on L ≈ 110 lattices. A detailed investigation of the probability distribution functions of the spin and link overlap, as well as of their correlation functions, shows that Replica Symmetry Breaking is the appropriate theoretical framework for the physically relevant length scales. Besides, we improve over existing methodologies to ensure equilibration in parallel tempering simulations.