## Matching experiments and theory in spin glasses

### Beatriz Seoane Bartolomé (LPT-ENS, Paris)

The unifying feature of glass formers (such as polymers, supercooled liquids, colloids, granular materials, spin glasses, superconductors, …) is a sluggish dynamics at low temperatures. Indeed, their dynamics is so slow that thermal equilibrium is never reached in macroscopic samples: in analogy with living beings, glasses are said to age. This fact suppose a difficulty to describe these systems theoretically. The reasons are two fold. One the one hand, most of the calculations are obtained in the experimentally unreachable low-temperature equilibrium, and on the other hand, they concern microscopic observables (obtained mainly with the replica method) that are hard to measure in experiments. In two recent works [1,2], we have shown that it is possible to quantitatively relate both realms, using large-scale simulations on the** special-purpose computers Janus and Janus II**, two dedicated supercomputers to simulate spin-glasses.

In the first work [1], we have performed a very accurate computation of the non-equilibrium fluctuation-dissipation ratio for the three-dimensional Edwards-Anderson Ising spin glass. This ratio (computed for finite times on very large, effectively infinite, systems) is compared with the equilibrium probability distribution of the spin overlap for finite sizes. The resulting **quantitative statics-dynamics dictionary**, based on observables that can be measured with current experimental methods, could allow the experimental exploration of important features of the spin-glass phase without uncontrollable extrapolations to infinite times or system sizes.

On the other hand, in Ref. [2], we have **reproduced in simulations a milestone experiment that measures the spin-glass 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 of amorphous Ge:Mn films [3]. 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, non-linear susceptibilities, recently measured in glass-forming liquids, scale as powers of the same microscopic length.

*Probing the spin-glass phase with non-equilibrium measurements: statics-dynamics equivalence through the fluctuation-dissipation ratio »*, accepted for PNAS, https://arxiv.org/abs/1610.01418

*Matching microscopic and macroscopic responses in glasses »*, under review in PRL.

*Magnetic Field Dependence of Spin Glass Free Energy Barriers »*, under review in PRL.