Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

Wang, Chi-Jen; Liu, Da-Jiang; Evans, James W.

doi:10.1063/1.4918908

Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

Journal Article · Tue Apr 28 04:00:00 EDT 2015 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4918908· OSTI ID:22415697

Wang, Chi-Jen ^[1]; Liu, Da-Jiang ^[1]; Evans, James W. ^[1]

Ames Laboratory–USDOE, Iowa State University, Ames, Iowa 50011 (United States)

Threshold versions of Schloegl’s model on a lattice, which involve autocatalytic creation and spontaneous annihilation of particles, can provide a simple prototype for discontinuous non-equilibrium phase transitions. These models are equivalent to so-called threshold contact processes. A discontinuous transition between populated and vacuum states can occur selecting a threshold of N ≥ 2 for the minimum number, N, of neighboring particles enabling autocatalytic creation at an empty site. Fundamental open questions remain given the lack of a thermodynamic framework for analysis. For a square lattice with N = 2, we show that phase coexistence occurs not at a unique value but for a finite range of particle annihilation rate (the natural control parameter). This generic two-phase coexistence also persists when perturbing the model to allow spontaneous particle creation. Such behavior contrasts both the Gibbs phase rule for thermodynamic systems and also previous analysis for this model. We find metastability near the transition corresponding to a non-zero effective line tension, also contrasting previously suggested critical behavior. Mean-field type analysis, extended to treat spatially heterogeneous states, further elucidates model behavior.

OSTI ID:: 22415697

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 16 Vol. 142; ISSN JCPSA6; ISSN 0021-9606

Country of Publication:: United States

Language:: English

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