# Matching microscopic and macroscopic responses in glasses

## TL;DR

This paper demonstrates that microscopic correlation functions and macroscopic response measurements in glasses are quantitatively consistent, linking microscopic and macroscopic behaviors through scaling analysis and experiments on spin glasses.

## Contribution

It provides a quantitative scaling analysis connecting microscopic and macroscopic responses in glasses, validated by experiments on spin glasses and glass-forming liquids.

## Key findings

- Microscopic and macroscopic coherence lengths are quantitatively consistent.
- Scaling behavior links microscopic correlation functions with macroscopic responses.
- Non-linear susceptibilities scale as powers of the microscopic length.

## Abstract

We first reproduce on the Janus and Janus II computers 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 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, non-linear susceptibilities, recently measured in glass-forming liquids, scale as powers of the same microscopic length.