  We consider an active Ising model in which spins both diffuse and align on
lattice in one and two dimensions. The diffusion is biased so that plus or
minus spins hop preferably to the left or to the right, which generates a
flocking transition at low temperature/high density. We construct a
coarse-grained description of the model that predicts this transition to be a
first-order liquid-gas transition in the temperature-density ensemble, with a
critical density sent to infinity. In this first-order phase transition, the
magnetization is proportional to the liquid fraction and thus varies
continuously. Using microscopic simulations, we show that this theoretical
prediction holds in 2d whereas the fluctuations alter the transition in 1d,
preventing for instance any spontaneous symmetry breaking.
