Schloegl's second model for autocatalysis on hypercubic lattices: Dimension dependence of generic two-phase coexistence.
Schloegl's second model on a (d ≥ 2)-dimensional hypercubic lattice involves: (i) spontaneous annihilation of particles with rate p and (ii) autocatalytic creation of particles at vacant sites at a rate proportional to the number of suitable pairs of neighboring particles. This model provides a prototype for nonequilibrium discontinuous phase transitions. However, it also exhibits nontrivial generic two-phase coexistence: Stable populated and vacuum states coexist for a finite range, pf(d)<p<pe(d), spanned by the orientation-dependent stationary points for planar interfaces separating these states. Analysis of interface dynamics from kinetic Monte Carlo simulation and from discrete reaction-diffusion equations (dRDEs) obtained from truncation of the exact master equation, reveals that pe(f)∼0.2113765+ce(f)/d as d→∞, where Δc=ce-cf≈0.014. A metastable populated state persists above pe(d) up to a spinodal p=ps(d), which has a well-defined limit ps(d→∞)=1/4. The dRDEs display artificial propagation failure, absent in the stochastic model due to fluctuations. This feature is amplified for increasing d, thus complicating our analysis.
Ames Laboratory, USDOE, Iowa State University, Ames, Iowa 50011, USA.
Chi-Jen
CJ
Wang
Da-Jiang
DJ
Liu
J W
JW
Evans
D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D008956:Models, Chemical; D008958:Models, Molecular; D044367:Phase Transition
D003102:Colloids