Dynamic Facilitation Picture of a Higher-Order Glass Singularity

Abstract

We show that facilitated spin mixtures with a tunable facilitation reproduce, on a Bethe lattice, the simplest higher-order singularity scenario predicted by the mode-coupling theory (MCT) of liquid-glass transition. Depending on the facilitation strength, they yield either a discontinuous glass transition or a continuous one, with no underlying thermodynamic singularity. Similar results are obtained for facilitated spin models on a diluted Bethe lattice. The mechanism of dynamical arrest in these systems can be interpreted in terms of bootstrap and standard percolation and corresponds to a crossover from a compact to a fractal structure of the incipient spanning cluster of frozen spins. Theoretical and numerical simulation results are fully consistent with MCT predictions. Although the glassy state of matter has been a long-time fascinating topic for physicists, it still presents several mysterious aspects [1]. Perhaps, the most controversial one is the very nature of the glass transition: that is the question of whether vitrification is a purely dynamical process or rather the (dynamical) manifestation of a genuine thermodynamic amorphous phase. In spite of much progress (for reviews, see [2][3][4][5][6]) the problem remains widely open. On one hand, there are notorious experimental and computational difficulties related to the exceedingly long equilibration times of macroscopic samples, and to the possibility of detecting unambiguously the elusive ''amorphous order.'' On the other hand, theoretical modeling of glassy systems has made clear that slow relaxation processes are ubiquitous and may result from very distinct mechanisms.

Crossover fromβtoαRelaxation in Cooperative Facilitation Dynamics

“…In this Letter we provide a test of the crossover scaling in the cooperative facilitation scenario (CFS) [8]. Several results have already suggested a close analogy between MCT and CFS [9][10][11][12]. Here we show that this relation is, in fact, quantitative and deep.…”

Cooperative heterogeneous facilitation: Multiple glassy states and glass-glass transition

“…(7) MCT features, although some ingenuity may be required. It has already been shown, for example, that the F 12 scenario is faithfully reproduced in this framework [36,37]. To substantiate the above observation, I now will focus on the next higher-order glass singularity, which is the F 13 scenario.…”

“…Figure 2 reports the behavior of the fraction of frozen spins, which is the analog of the nonergodicity parameter in the facilitation approach, when the temperature crosses the liquidglass continuous transition and the glass-glass transition. This quantity can be exactly computed from B [36,37], and its expression is not reported here; we only notice that its general features, and in particular the scaling properties near the critical states, are similar to those of B. We observe that the fraction of frozen spins first increases smoothly at the liquid-glass continuous transition and then suddenly jumps at the glass-glass transition.…”

Mean field theory of the swap Monte Carlo algorithm

“…Under this assumptions, the theory describes well the qualitative behavior of the relaxation time in finite dimensions [5,32,33]. Furthermore, on the Bethe lattice, the Fredrickson-Andersen (FA) model [34], which is a typical model in the DFT class, exhibits very similar behavior to the MCT [35][36][37][38][39][40]. Also, in finite dimensions, a Kac version of the FA model describes well the avoided dynamical transition [41].…”