Coexistence of metastable phases in states with a current

Such states are obtained as stationary solutions of an integro-differential equation derived by Giacomin and Lebowitz from Ising systems with Kac potential and Kawasaki dynamics. In the thermodynamic limit they are described by magnetization profiles whose values lie almost everywhere in the metastable region, positive and negative magnetization regions being separated by a sharp interface. When instead no currents are imposed the state relaxes to a Wulff shape.