Fibrillar templates and soft phases in systems with short-range dipolar and long-range interactions

We analyze the thermal fluctuations of particles that have a short-range dipolar attraction and a long-range repulsion. In an inhomogeneous particle density region, or "soft phase," filamentary patterns appear which are destroyed only at very high temperatures. The filaments act as a fluctuating template for correlated percolation in which low-energy excitations can move through the stable pattern by local rearrangements. At intermediate temperatures, dynamically averaged checkerboard states appear. We discuss possible implications for cuprate superconducting and related materials.