  We introduce a generalized Hamiltonian Mean Field Model (gHMF)-XY model with
both linear and quadratic coupling between spins and explicit Hamiltonian
dynamics. In addition to the usual paramagnetic and ferromagnetic phases, this
model also possesses a nematic phase. The gHMF can be solved explicitly using
Boltzmann-Gibbs (BG) statistical mechanics, in both canonical and
microcanonical ensembles. However, when the resulting microcanonical phase
diagram is compared with the one obtained using molecular dynamics simulations,
it is found that the two are very different. We will present a dynamical theory
which allows us to explicitly calculate the phase diagram obtained using
molecular dynamics simulations without any adjustable parameters. The model
illustrates the fundamental role played by dynamics as well the inadequacy of
BG statistics for systems with long-range forces in the thermodynamic limit.
