Extended Data Fig. 3: Characteristic temperatures from glassy dynamics.
From: Ideal non-crystals as a distinct form of ordered states without symmetry breaking
The dynamics of our ideal-non-crystal system is studied using molecular dynamics simulations via LAMMPS. The structure relaxation is measured by the self-intermediate scattering function \({F}_{s}(k,t)=\langle {\Sigma }_{j}\,\exp ({\rm{i}}\cdot [{\underline{{\boldsymbol{r}}}}_{\rm{j}}({\rm{t}})-{\underline{{\boldsymbol{r}}}}_{\rm{j}}(0)])/{\rm{N}}\rangle\), where k = ∣k∣ corresponds to the first peak of the static structure factor and \(\langle \cot \rangle\) denotes the time average. The relative position \({\underline{{\boldsymbol{r}}}}_{j}(t)={{\boldsymbol{r}}}_{j}(t)-{\Sigma }_{k}\,{{\boldsymbol{r}}}_{k}(t)/{n}_{j}\) is used to remove long-wavelength Mermin-Wagner fluctuations in 2D, with the summation running over all neighbours of particle j. The structure relaxation time τα is defined by Fs(k, τα) = e−1. a, Self-intermediate scattering function Fs(k, t) for different temperatures. The dashed line indicates Fs(k, t) = e−1. b, τα as a function of 1/T. The solid line shows an Arrhenius fit to the high-temperature data \({\tau }_{\alpha } \sim \exp (\Delta E/T)\). The estimated onset temperature of sluggish glassy dynamics Ton = 2.4 × 10−3 is indicated by the dashed line. c, τα as a function of T. The solid line is a fit of data below Ton according to the Vogel-Fulcher-Tammann (VFT) law \({\tau }_{\alpha } \sim \exp [D{T}_{{\rm{VFT}}}/(T-{T}_{{\rm{VFT}}})]\), from which we extract the hypothesised ideal glass transition temperature TVFT = 9.12 × 10−4, with D as a fitting parameter. Ton and TVFT provide two reference temperatures for our system.
