Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field.

The very existence of a phase transition for spin glasses in an external magnetic field is controversial, even in high dimensions. We carry out massive simulations of the Ising spin-glass in a field, in six dimensions (which, according to classical-but not generally accepted-field-theoretical studies, is the upper critical dimension). We obtain results compatible with a second-order phase transition and estimate its critical exponents for the simulated lattice sizes. The detailed analysis performed by other authors of the replica symmetric Hamiltonian, under the hypothesis of critical behavior, predicts that the ratio of the renormalized coupling constants remain bounded as the correlation length grows. Our numerical results are in agreement with this expectation.

Scaling Law Describes the Spin-Glass Response in Theory, Experiments, and Simulations.

The correlation length ξ, a key quantity in glassy dynamics, can now be precisely measured for spin glasses both in experiments and in simulations. However, known analysis methods lead to discrepancies either for large external fields or close to the glass temperature. We solve this problem by introducing a scaling law that takes into account both the magnetic field and the time-dependent spin-glass correlation length. The scaling law is successfully tested against experimental measurements in a CuMn single crystal and against large-scale simulations on the Janus II dedicated computer.

Aging Rate of Spin Glasses from Simulations Matches Experiments.

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.

Numerical Construction of the Aizenman-Wehr Metastate.

Chaotic size dependence makes it extremely difficult to take the thermodynamic limit in disordered systems. Instead, the metastate, which is a distribution over thermodynamic states, might have a smooth limit. So far, studies of the metastate have been mostly mathematical. We present a numerical construction of the metastate for the d=3 Ising spin glass. We work in equilibrium, below the critical temperature. Leveraging recent rigorous results, our numerical analysis gives evidence for a dispersed metastate, supported on many thermodynamic states.