Lattice field theories with an energy current

We investigate a lattice scalar field theory in the presence of a bias favo uring the establishment of an energy current, as a model for stationary non -equilibrium processes at low temperature in a non-integrable system. There is a transition at a finite value of the bias to a gapless modulated phase which carries a classical current; however, unlike in similar, integrable, models, quantum effects also allow for a non-zero current at arbitrarily s mall bias. The transition is second-order in the magnetically disordered ph ase, but is pre-empted by a first-order transition in the ferromagnetic cas e, at least at the mean-field level. (C) 2000 Elsevier Science B.V. All rig hts reserved.