Structural transitions, melting, and intermediate phases for stripe- and clump-forming systems.

We numerically examine the properties of a two-dimensional system of particles which have competing long-range repulsive and short-range attractive interactions as a function of density and temperature. For increasing density, there are well-defined transitions between a low-density clump phase, an intermediate stripe phase, an anticlump phase, and a high-density uniform phase. To characterize the transitions between these phases we propose several measures which take into account the different length scales in the system. For increasing temperature, we find an intermediate phase that is liquidlike on the short length scale of interparticle spacing but solidlike on the larger length scale of the clump, stripe, or anticlump pattern. This intermediate phase persists over the widest temperature range in the stripe phase when the local particle lattice within an individual stripe melts well below the temperature at which the entire stripe structure breaks down, and is characterized by intrastripe diffusion of particles without interstripe diffusion. This is followed at higher temperatures by the onset of interstripe diffusion in an anisotropic diffusion phase and then by breakup of the stripe structure. We identify the transitions between these regimes through diffusion, heat capacity, and energy fluctuation measurements and find that within the intrastripe liquid regime, the excess entropy goes into disordering the particle arrangements within the stripe rather than affecting the stripe structure itself. The clump and anticlump phases also show multiple temperature-induced diffusive regimes which are not as pronounced as those of the stripe phase.