  We investigate nuclear pasta structures at high temperatures in the framework
of relativistic mean field model with Thomas-Fermi approximation. Typical pasta
structures (droplet, rod, slab, tube, and bubble) are obtained, which form
various crystalline configurations. The properties of those nuclear pastas are
examined in a three-dimensional geometry with reflection symmetry, where the
optimum lattice constants are fixed by reproducing the droplet/bubble density
that minimizes the free energy adopting spherical or cylindrical approximations
for Wigner-Seitz cells. It is found that different crystalline structures can
evolve into each other via volume conserving deformations. For fixed densities
and temperatures, the differences of the free energies per baryon of nuclear
pasta in various shapes and lattice structures are typically on the order of
tens of keV, suggesting the possible coexistence of those structures. As
temperature increases, the thermodynamic fluctuations are expected to disrupt
the long-range ordering in nuclear pasta structures. We then estimate the
critical conditions for nuclear pasta to become disordered and behave like
liquid, which are found to be sensitive to the densities, temperatures, proton
fractions, and nuclear shapes. If we further increase temperature, eventually
the nonuniform structures of nuclear pasta become unstable and are converted
into uniform nuclear matter. The phase diagrams of nuclear matter are then
estimated, which should be useful for understanding the evolutions of neutron
stars, supernova dynamics, and binary neutron star mergers.
