Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have