  We investigate a lattice scalar field theory in the presence of a bias
favouring the establishment of an energy current, as a model for stationary
nonequilibrium 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 small
bias. The transition is second order in the magnetically disordered phase, but
is pre-empted by a first-order transition in the ferromagnetic case, at least
at the mean-field level.
