  The Ising model for a ferromagnet and the lattice gas model for a fluid are
equivalent in thermodynamics but different in dynamics. The order parameter in
the lattice gas is conserved while the order parameter in the Ising ferromagnet
is not. As a result, two fluid phases with different densities always coexist
in equilibrium, while two magnetic phases with opposite orientations only
coexist in a metastable state. The non-conserved nature of the Ising order
parameter results in the phenomenon of "phase bullying," when one phase grows
at the expense of another one. We show that even a small probability for the
order parameter to exhibit Ising dynamics breaks the particle conservation law
thus resulting in phase bullying. We characterized this phenomenon by the
probability of Ising dynamics, distance to the critical point, and system size.
