Phase-ordering kinetics in the Allen-Cahn (Model A) class: Universal aspects elucidated by electrically induced transition in liquid crystals

Opinion inertia and coarsening in the persistent voter model

We consider the persistent voter model (PVM), a variant of the voter model (VM) that includes transient, dynamically induced zealots. Due to peer reinforcement, the internal confidence η_{i} of a normal voter increases in steps of size Δη. Once it surpasses a given threshold, it becomes a zealot. Its opinion remains frozen until enough interactions with the opposing opinion occur, resetting its confidence. No longer a zealot, the regular voter may change opinion once again. This mechanism of opinion inertia, though simplified, is responsible for an effective surface tension, and the PVM exhibits a crossover from a fluctuation-driven dynamics, as in the VM, to a curvature-driven one, akin to the Ising model at low temperature. The average time τ to attain consensus is nonmonotonic with respect to Δη and reaches a minimum at Δη_{min}. In this paper we elucidate the mechanisms that accelerate the system towards consensus close to Δη_{min}. Near the crossover at Δη_{min}, the intermediate region around the domains where the regular voters accumulate (the active region, AR) is large. The surface tension, albeit small, is sufficient to maintain the shape and reduce the domain fragmentation. The large size of the AR in the region of Δη_{min} has two important effects that accelerate the dynamics. First, it dislodges the zealots within the bulk of the domains. Secondly, it maximally suppresses the formation of slowly evolving stripes typical in Ising-like models. This suggests the importance of understanding the role of the AR, where opinion changes are facilitated, and the interplay between regular voters and zealots in disrupting polarized states.

Ordering kinetics and steady states of XY-model with ferromagnetic and nematic interaction

Previous studies on the generalized XY model have concentrated on the equilibrium phase diagram and the equilibrium nature of distinct phases under varying parameter conditions. We direct our attention towards examining the system's evolution towards equilibrium states across different parameter values, specifically by varying the relative strengths of ferromagnetic and nematic interactions. We study the kinetics of the system, using the temporal annihilation of defects at varying temperatures and its impact on the coarsening behavior of the system. For both pure polar and pure nematic systems, we observe temperature-dependent decay of the exponent, leading to a decelerated growth of domains within the system. At parameter values where both ferromagnetic and nematic interactions are simultaneously present, we show a phase diagram highlighting three low-temperature phases-polar, nematic, and coexistence-along- side a high-temperature disordered phase. Our study provides valuable insights into the complex interplay of interactions, offering a comprehensive understanding of the system's behavior during its evolution towards equilibrium.

Critical Percolation in the Ordering Kinetics of Twisted Nematic Phases

I report on the experimental confirmation that critical percolation statistics underlie the ordering kinetics of twisted nematic phases in the Allen-Cahn universality class. Soon after the ordering starts from a homogeneous disordered phase and proceeds toward a broken Z_{2}-symmetry phase, the system seems to be attracted to the random percolation fixed point at a special timescale t_{p}. At this time, exact formulas for crossing probabilities in percolation theory agree with the corresponding probabilities in the experimental data. The ensuing evolution for the number density of hull-enclosed areas is described by an exact expression derived from a percolation model endowed with curvature-driven interface motion. Scaling relation for hull-enclosed areas versus perimeters reveals that the fractal percolation geometry is progressively morphed into a regular geometry up to the order of the classical coarsening length. In view of its universality and experimental possibilities, the study opens a path for exploring percolation keystones in the realm of nonequilibrium, phase-ordering systems.

Energy-lowering and constant-energy spin flips: Emergence of the percolating cluster in the kinetic Ising model

After a sudden quench from the disordered high-temperature T_{0}→∞ phase to a final temperature well below the critical point T_{F}≪T_{c}, the nonconserved order parameter dynamics of the two-dimensional ferromagnetic Ising model on a square lattice initially approaches the critical percolation state before entering the coarsening regime. This approach involves two timescales associated with the first appearance (at time t_{p_{1}}>0) and stabilization (at time t_{p}>t_{p_{1}}) of a giant percolation cluster, as previously reported. However, the microscopic mechanisms that control such timescales are not yet fully understood. In this paper, to study their role on each time regime after the quench (T_{F}=0), we distinguish between spin flips that decrease the total energy of the system from those that keep it constant, the latter being parametrized by the probability p. We show that observables such as the cluster size heterogeneity H(t,p) and the typical domain size ℓ(t,p) have no dependence on p in the first time regime up to t_{p_{1}}. Furthermore, when energy-decreasing flips are forbidden while allowing constant-energy flips, the kinetics is essentially frozen after the quench and there is no percolation event whatsoever. Taken together, these results indicate that the emergence of the first percolating cluster at t_{p_{1}} is completely driven by energy decreasing flips. However, the time for stabilizing a percolating cluster is controlled by the acceptance probability of constant-energy flips: t_{p}(p)∼p^{-1} for p≪1 (at p=0, the dynamics gets stuck in a metastable state). These flips are also the relevant ones in the later coarsening regime where dynamical scaling takes place. Because the phenomenology on the approach to the percolation point seems to be shared by many 2D systems with a nonconserved order parameter dynamics (and certain cases of conserved ones as well), our results may suggest a simple and effective way to set, through the dynamics itself, t_{p_{1}} and t_{p} in such systems.

Steady states and coarsening in one-dimensional driven Allen-Cahn system

We study the steady states and the coarsening dynamics in a one-dimensional driven nonconserved system modeled by the so-called driven Allen-Cahn equation, which is the standard Allen-Cahn equation with an additional driving force. In particular, we derive equations of motion for the phase boundaries in a phase ordering system obeying this equation using a nearest-neighbor interaction approach. Using the equations of motion we explore kink binary and ternary interactions and analyze how the average domain size scale with respect to time. Further, we employ numerical techniques to perform a bifurcation analysis of the one-period stationary solutions of the equation. We then investigate the linear stability of the two-period solutions and thereby identify and study various coarsening modes.