Event-chain Monte Carlo simulations of the liquid to solid transition of two-dimensional decagonal colloidal quasicrystals.

In event-chain Monte Carlo simulations, we model colloidal particles in two dimensions that interact according to an isotropic short-ranged pair potential which supports the two typical length scales present in decagonal quasicrystals. We investigate the assembled structures as we vary the density and temperature. Our special interest is related to the transition from quasicrystal to liquid.

Quantum Criticality of Two-Dimensional Quantum Magnets with Long-Range Interactions.

We study the critical breakdown of two-dimensional quantum magnets in the presence of algebraically decaying long-range interactions by investigating the transverse-field Ising model on the square and triangular lattice. This is achieved technically by combining perturbative continuous unitary transformations with classical Monte Carlo simulations to extract high-order series for the one-particle excitations in the high-field quantum paramagnet. We find that the unfrustrated systems change from mean-field to nearest-neighbor universality with continuously varying critical exponents.

A kinetic-Monte Carlo perspective on active matter.

We study non-equilibrium phases for interacting two-dimensional self-propelled particles with isotropic pair-wise interactions using a persistent kinetic Monte Carlo approach. We establish the quantitative phase diagram, including the motility-induced phase separation (MIPS) that is a commonly observed collective phenomenon in active matter. In addition, we demonstrate for several different potential forms the presence of two-step melting, with an intermediate hexatic phase, in regions far from equilibrium.

Nonequilibrium steady states, coexistence, and criticality in driven quasi-two-dimensional granular matter.

Nonequilibrium steady states of vibrated inelastic frictionless spheres are investigated in quasi-two-dimensional confinement via molecular dynamics simulations. The phase diagram in the density-amplitude plane exhibits a fluidlike disordered and an ordered phase with threefold symmetry, as well as phase coexistence between the two. A dynamical mechanism exists that brings about metastable traveling clusters and at the same time stable clusters with anisotropic shapes at low vibration amplitude.

Universal hidden order in amorphous cellular geometries.

Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as the optimisation of the moment of inertia of Voronoi cells, i.e.