Matching Microscopic and Macroscopic Responses in Glasses

Abstract

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.

Slowing down of spin glass correlation length growth: Simulations meet experiments

“…where d f is the fractal dimension equal to d f = d − θ/2 (d = 3 is the space dimension, while θ is the socalled replicon exponent [19]). Because at the correlation lengths of interest θ ≈ 0.3, the approximation d f ≈ d made in previous work (Ref.…”

Effect of magnetic fields on spin glass dynamics

“…As pointed out in Ref. 20 , the correlated space is in fact fractal, with a dimensionality exponent of ∼ 2.81 instead of 3. This has the effect of replacing L 3 in Eqs.…”

“…By varying L, and measuring the coefficient of the H 2 reduction in ∆ max (H, L), one can uniquely detect the difference between compact and fractal growth through the measured exponent of L in Eq. (20). The relatively small value of the changes in ∆ max (H, L)/k B exhibited in Table I make this a somewhat daunting, but still possible task.…”

“…For example, is the growth of the correlated regions compact or fractal 20 ? Now that the scaling factor b has been fixed, it should be possible to compare the number of correlated spins as a function of film thickness L, and in that way determine the nature of the growth of ξ(t, T ).…”

“…Earlier work 6,8,19,20 has shown that an applied magnetic field reduces the barrier heights in a spin glass according to the strength of the Zeeman interaction upon the correlated states, E Z . Simply stated,…”