  Using classical Monte Carlo simulations, we study a simple statistical
mechanical model of relevance to the emergence of polarisation from local
displacements on the square and cubic lattices. Our model contains two key
ingredients: a Kitaev-like orientation-dependent interaction between nearest
neighbours, and a steric term that acts between next-nearest neighbours. Taken
by themselves, each of these two ingredients is incapable of driving long-range
symmetry breaking, despite the presence of a broad feature in the corresponding
heat capacity functions. Instead each component results in a "hidden"
transition on cooling to a manifold of degenerate states, the two manifolds are
different in the sense that they reflect distinct types of local order.
Remarkably, their intersection---\emph{i.e.} the ground state when both
interaction terms are included in the Hamiltonian---supports a spontaneous
polarisation. In this way, our study demonstrates how local ordering mechanisms
might be combined to break global inversion symmetry in a manner conceptually
similar to that operating in the "hybrid" improper ferroelectrics. We discuss
the relevance of our analysis to the emergence of spontaneous polarisation in
well-studied ferroelectrics such as BaTiO$_3$ and KNbO$_3$.
