Self-organized pattern formations from two-length-scale repulsive interactions

We investigated the self-organized pattern formations of particle clusters generated from two length scale isotropic repulsive interactions by using off-axis Monte-Carlo simulations. Increasing the density of particles, we obtained the conditions for the formation of long-range ordered structures such as chain structures, hexagonally arranged droplets, and aligned stripes. We studied the properties of the spontaneously ordered phases and the critical conditions of their phase transitions for various length ratios of the two-length-scale repulsive interactions. Our simulation results show that the ratio between the two length scales is an essential parameter for determining not only the critical conditions of the phase transitions but also the existence of long-range ordered structures. In particular, the transition phase behaviors become complicated when the ratio is small, and the system exhibits alternating droplet and stripe structures as the density changes.