The Physics of Phase Bullying.

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.