  A simple construction is presented, which generalises piecewise linear
one-dimensional Markov maps to an arbitrary number of dimensions. The
corresponding coupled map lattice, known as a simplicial mapping in the
mathematical literature, allows for an analytical investigation. Especially the
spin Hamiltonian, which is generated by the symbolic dynamics is accessible. As
an example a formal relation between a globally coupled system and an Ising
mean field model is established. The phase transition in the limit of infinite
system size is analysed and analytical results are compared with numerical
simulations.
