A novel class of nonequilibrium phase transitions at zero temperature is found in chains of nonlinear oscillators. For two paradigmatic systems, the Hamiltonian $XY$ model and the discrete nonlinear Schrödinger equation, we find that the application of boundary forces induces two synchronized phases, separated by a nontrivial interfacial region where the kinetic temperature is finite. Dynamics in such a supercritical state displays anomalous chaotic properties whereby some observables are nonextensive and transport is superdiffusive. At finite temperatures, the transition is smoothed, but the temperature profile is still nonmonotonic.

• Received 13 January 2014

DOI:https://doi.org/10.1103/PhysRevLett.112.134101