Two-Dimensional Crystals far from Equilibrium

Statistics of a granular cluster ensemble at a liquid-solid-like phase transition

We report on the construction of a granular network of particles to study the formation, evolution, and statistical properties of clusters of particles developing at the vicinity of a liquid-solid-like phase transition within a vertically vibrated quasi-two-dimensional granular system. Using the data of particle positions and local order from Castillo et al. [G. Castillo, N. Mujica, and R. Soto, Phys. Rev. Lett. 109, 095701 (2012)0031-900710.1103/PhysRevLett.109.095701], we extract granular clusters taken as communities of the granular network via modularity optimization. Each one of these communities is a patch of particles with a very well defined local orientational order embedded within an array of other patches forming a complex cluster network. The distributions of cluster sizes and lifespans for the cluster network depend on the distance to the liquid-solid-like phase transition of the quasi-two-dimensional granular system. Specifically, the cluster size distribution displays a scale-invariant behavior for at least a decade in cluster sizes, while cluster lifespans grow monotonically with each cluster size. We believe this systematic community analysis for clustering in granular systems can help to study and understand the spatiotemporal evolution of mesoscale structures in systems displaying out-of-equilibrium phase transitions.

Correlated noise and critical dimensions

In equilibrium, the Mermin-Wagner theorem prohibits the continuous symmetry breaking for all dimensions d≤2. In this work, we discuss that this limitation can be circumvented in nonequilibrium systems driven by the spatiotemporally long-range anticorrelated noise. We first compute the lower and upper critical dimensions of the O(n) model driven by the spatiotemporally correlated noise by means of the dimensional analysis. Next we consider the spherical model, which corresponds to the large-n limit of the O(n) model and allows us to compute the critical dimensions and critical exponents, analytically. Both results suggest that the critical dimensions increase when the noise is positively correlated in space and time and decrease when anticorrelated. We also report that the spherical model with the correlated noise shows the hyperuniformity and giant number fluctuation even well above the critical point.