Phase structure of the skyrme model

Using the Skyrme model of strong interactions we have found periodic static solutions of the Euler-Lagrange equations having a rectangular symmetry similar to that found in studies of neutron crystals. These solutions are found to undergo a second-order phase transition from a low-density phase of isolated skyrmions to a high-density phase in which individual skyrmions lose their identity and in which the unit cell average of the scalar field is rigorously zero. These solutions have the lowest energy of any yet found for the Skyrme model. Connections to physically interesting phase transitions in nuclear and solid state physics are discussed.