  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.
