Matching Microscopic and Macroscopic Responses in Glasses*

We use Janus and Janus II supercomputers to revisit two successful experimental approaches to detect the glass correlation length from macroscopic observables [1]. On the one hand, we reproduce a milestone experiment to measure spin-glass coherence length, ξ_max, through the lowering of free-energy barriers induced by the Zeeman effect [2], and on the other hand, we explore the relationship between the spin-glass coherence length and the macroscopic non-linear susceptibilities, the latter recently measured in supercooled glasses [3] to support the existence of a growth of thermodynamic amorphous order upon approaching the ideal glass transition. We compare these macroscopic measures, with the microscopic spin-glass coherence length ξ_mic (as extracted from the four-point spatial correlation function), concluding that (i) ξ_max and ξ_mic are mutually consistent, and (ii) the non-linear susceptibilities scale as powers of ξ_mic, so they can be used to describe the growth of an amorphous order in glass formers. In addition, we propose scaling laws on the applied field that have allowed a quantitative analysis of new experiments [4].

[1] Janus Collaboration, Phys. Rev. Lett. 118, 157202 (2017).
[2] Y. G. Joh, R. Orbach, G. G. Wood, J. Hammann, and
E. Vincent, Phys. Rev. Lett. 82, 438 (1999).
[3] S. Albert, T. Bauer, M. Michl, G. Biroli, J.-P. Bouchaud,
A. Loidl, P. Lunkenheimer, R. Tourbot, C. WiertelGasquet,
and F. Ladieu, Science 352, 1308 (2016).
[4] S. Guchhait and R. Orbach, Phys. Rev. Lett. 118, 157203 (2017).