| Abstract: |
| Discontinuous phase transitions are common in the steady states of diverse non-equilibrium systems describing catalytic reaction-diffusion processes, biological transport, spatial epidemics, etc. Behavior in spatially continuous formulations, described by reaction-diffusion type equations (RDEs), often mimics that of classic equilibrium van der Waals type systems. When accounting for noise, similarities include a discontinuous phase transition at some value, $p_{eq}$, of a control parameter, $p$, with metastability and hysteresis around $p_{eq}$. For each $p$, there is a unique critical droplet of the more stable phase embedded in the less stable or metastable phase which is stationary (neither shrinking nor growing), and with size diverging as $p\to p_{eq}$. Spatially discrete analogs of mean-field formulations, described by lattice differential equations (LDEs), are more appropriate for some applications, but have received less attention. It is recognized that LDEs can exhibit richer behavior than RDEs, specifically propagation failure for planar interphases separating distinct phases. We show that the occurrence of entire families of stationary droplets result from this feature. The extent of these families increases as $p\to p_{eq}$ and can be infinite if propagation failure is realized. In addition, there exists a regime of generic two-phase coexistence where arbitrarily large droplets of either phase always shrink eventurally. Such rich behavior is qualitatively distinct from that for classic nucleation in equilibrium and spatially continuous nonequilibrium systems. |
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