Colloidal test bed for universal dynamics of phase transitions

Abstract

Early insight on the critical dynamics of phase transitions arose in a cosmological setting in an effort to understand the origin of structure formation in the early Universe. Kibble pointed out that in a spontaneous symmetry breaking scenario, when a system is driven across a phase transition from a high-symmetry phase to a topologically nontrivial vacuum manifold, causally disconnected regions of the system choose independently the broken symmetry (1,2). These conflicting choices result in the formation of topological defects, such as domain walls in a ferromagnet and vortices in a superfluid, to name a couple of familiar examples. Soon after, Zurek indicated that signatures of universality in the dynamics of a phase transition could be tested in condensed matter systems, e.g., superfluid Helium (3,4). Further, he improved the estimate for the average size of the domains and predicted a universal power law for the density of topological defects as a function of the rate at which the phase transition is crossed. The combination of these ideas is known as the Kibble-Zurek mechanism (KZM) and has been a lively subject of both theoretical and experimental research during the last decades. The abundant attempts to verify the KZM in the laboratory have however faced a variety of shortcomings and while different aspects of the mechanism have been confirmed, a definite test is still missing (5). A remarkable step forward is reported in this issue by Deutschländer et al., who used colloidal monolayers as a test bed for universal critical dyamics with unprecedented accuracy (6).

Bond-orientational order and Frank’s constant in two-dimensional colloidal hard spheres

“…Here a is a constant, φ h the area fraction where the system becomes fully hexatic, and the exponent ν = 1/2 [11,40,41]. As seen in figure 3(b), the data are very well described by this expression and from the fit we obtain a value for φ h = 0.696, which is in excellent agreement with the start of the hexatic phase at φ = 0.70 [36].…”

“…Upon approaching the hexatic phase from the liquid, it has been shown that the bond-orientational correlation length diverges [11]. Consequently, it is also expected that the corresponding bond-orientational correlation time, τ 6 , diverges [11,40,41]. We determine τ 6 from the bond-orientational correlation functions g 6 (t), shown in figure 3(a) for a tilt angle of α = 0.25 • [36], via g 6 (t) ∼ exp(−t/τ 6 ).…”

“…In our case, however, this divergence is preempted by a weakly first order phase transition and hence the bond-orientational correlation time does not diverge. Nevertheless, we can still describe the onset of the divergence of τ 6 for area fractions below the coexistence region using [11,40,41]…”

“…where the hexatic phase is predicted to become unstable. As the area fraction increases, Frank's constant sharply increases and its divergence can be described by [11,40,41]…”

Distribution of Kinks in an Ising Ferromagnet After Annealing and the Generalized Kibble-Zurek Mechanism

“…A cooling schedule cannot possibly involve the crossing of the critical point considered in the original studies of KZM. However, the KZM prediction can be extended to account for "half-quenches" ending at the critical point [48][49][50][51][52]. At the same time, the finitetemperature treatment endows the dynamic with coarsening.…”