Schloegl's second model for autocatalysis on hypercubic lattices: Dimension dependence of generic two-phase coexistence

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.