Droplet formation near first-order phase transitions: A mechanism for   heterogeneity and phase separation away from the coexistence curve
  Phase separation, i.e., the coexistence of two different phases, is observed in many systems away from the coexistence curve of a first-order transition, leading to a stable heterogeneous phase or region. Examples include various quantum ferromagnets, heavy-fermion systems, rare-earth nickelates, and others. These observations seem to violate basic notions of equilibrium thermodynamics, which state that phase separation can occur only on the coexistence curve. We show theoretically that quenched disorder allows for phase separation away from the coexistence curve even in equilibrium due to the existence of stable minority-phase droplets within the majority phase. Our scenario also answers a related question: How can a first-order transition remain sharp in the presence of quenched disorder without violating the rigorous lower bound $\nu \geq 2/d$ for the correlation-length exponent? We discuss this scenario in the context of experimental results for a large variety of systems. 
T.R. Kirkpatrick and D. Belitz
cond-mat.str-el cond-mat.stat-mech