Nonequilibrium Phase Transition To Temporal Oscillations In Mean-Field Spin Models

We propose a mean-field theory for nonequilibrium phase transitions to a periodically oscillating state in spin models. A nonequilibrium generalization of the Landau free energy is obtained from the join distribution of the magnetization and its smoothed stochastic time derivative. The order parameter of the transition is a Hamiltonian, whose nonzero value signals the onset of oscillations. The Hamiltonian and the nonequilibrium Landau free energy are determined explicitly from the stochastic spin dynamics. The oscillating phase is also characterized by a non-trivial overlap distribution reminiscent of a continuous replica symmetry breaking, in spite of the absence of disorder. An illustration is given on an explicit kinetic mean-field spin model.