Scanning-probe and information-concealing machine learning intermediate hexatic phase and critical scaling of solid-hexatic phase transition in deformable particles

We investigate the two-dimensional melting of deformable polymeric particles with multi-body interactions described by the Voronoi model. We report machine learning evidence for the existence of the intermediate hexatic phase in this system, and extract the critical exponent $\nu\approx0.65$ for the divergence of the correlation length of the associated solid-hexatic phase transition. Moreover, we clarify the discontinuous nature of the hexatic-liquid phase transition in this system. These findings are achieved by directly analyzing system's spatial configurations with two generic machine learning approaches developed in this work, dubbed ``scanning-probe'' via which the possible existence of intermediate phases can be efficiently detected, and ``information-concealing'' via which the critical scaling of the correlation length in the vicinity of generic continuous phase transition can be extracted. Our work provides new physical insights into the fundamental nature of the two-dimensional melting of deformable particles, and establishes a new type of generic toolbox to investigate fundamental properties of phase transitions in various complex systems.

Emergence and melting of active vortex crystals

Melting of two-dimensional (2D) equilibrium crystals is a complex phenomenon characterized by the sequential loss of positional and orientational order. In contrast to passive systems, active crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Currently, the non-equilibrium physics of active crystallization and melting processes is not well understood. Here, we establish the emergence and investigate the melting of self-organized vortex crystals in 2D active fluids using a generalized Toner-Tu theory. Performing extensive hydrodynamic simulations, we find rich transition scenarios. On small domains, we identify a hysteretic transition as well as a transition featuring temporal coexistence of active vortex lattices and active turbulence, both of which can be controlled by self-propulsion and active stresses. On large domains, an active vortex crystal with solid order forms within the parameter range corresponding to active vortex lattices. The melting of this crystal proceeds through an intermediate hexatic phase. Generally, these results highlight the differences and similarities between crystalline phases in active fluids and their equilibrium counterparts.

Laser-induced melting of two-dimensional dusty plasma system in RF discharge

We present a detailed analysis of experimental study, which shows clear evidence of a two-stage melting process of a quasi-two-dimensional dusty plasma system in a high-frequency gas discharge. We accurately calculated global parameters of the orientational and translational order, as well as their susceptibilities to determine two critical points, related to “solid-to-hexatic” and “hexatic-to-liquid” phase transitions. The nature of the emerging defects and changes in their mutual concentration, in addition to the estimate of core energy of free dislocations also counts in favor of the formation of an intermediate hexatic phase. These results are fully consistent with the Berezinsky–Kosterlitz–Thouless theory.

Dynamical arrest of topological defects in 2D hyperuniform disk packings

We investigate collective motions of points in 2D systems, orchestrated by Lloyd algorithm. The algorithm iteratively updates a system by minimising the total quantizer energy of the Voronoi landscape of the system. As a result of a tradeoff between energy minimisation and geometric frustration, we find that optimised systems exhibit a defective landscape along the process, where strands of 5- and 7-coordinated dislocations are embedded in the hexatic phase. In particular, dipole defects, each of which is the simplest possible pair of a pentagon and a heptagon, come into the picture of dynamical arrest, as the system freezes down to a disordered hyperuniform state. Moreover, we explore the packing fractions of 2D disk packings associated to the obtained hyperuniform systems by considering the maximum inscribed disks in their Voronoi cells.

Hexatic phase in a model of active biological tissues

Epithelial cell tissues undergo a solid–liquid transition, e.g. as the motility of the cells increases. We find an intermediate hexatic phase in between the solid and the liquid ones, and the transition to follow the KTHNY scenario.