  We introduce a strategy to write down lattice models of spin rotational
symmetric Hamiltonians with arbitrary spin-$S$ that are Marshall positive and
can be simulated efficiently using world line Monte Carlo methods. As an
application of our approach we consider a square lattice $S=1$ model for which
we design a $3\times 3$ - spin plaquette interaction. By numerical simulations
we establish that our model realizes a novel "Haldane nematic" phase that
breaks lattice rotational symmetry by the spontaneous formation of Haldane
chains, while preserving spin rotations, time reversal and lattice
translations. By supplementing our model with a two-spin Heisenberg
interaction, we present a study of the transition between N\'eel and Haldane
nematic phase, which we find to be of first order.
