  We construct a mixing continuous piecewise linear map on [-1,1] with the
property that a two-dimensional lattice made of these maps with a linear north
and east nearest neighbour coupling admits a phase transition. We also provide
a modification of this construction where the local map is an expanding
analytic circle map. The basic strategy is borroughed from [Gielis-MacKay
(2000)], namely we compare the dynamics of the CML to those of a probabilistic
cellular automaton of Toom's type.
