We analyze a discontinuous nonequilibrium phase transition between an active (or reactive) state and a poisoned (or extinguished) state occurring in a stochastic lattice-gas realization of Schloegl’s second model for autocatalysis. This realization, also known as the quadratic contact process, involves spontaneous annihilation, autocatalytic creation, and diffusion of particles on a square lattice, where creation at empty sites requires a suitable nearby pair of particles. The poisoned state exists for all annihilation rates and is an absorbing particle-free “vacuum” state. The populated active steady state exists only for below a critical value, . If denotes the critical value below which a finite population can survive, then we show that . This strict inequality contrasts a postulate of Durrett, and is a direct consequence of the occurrence of coexisting stable active and poisoned states for a finite range (which shrinks with increasing diffusivity). This so-called generic two-phase coexistence markedly contrasts behavior in thermodynamic systems. However, one still finds metastability and nucleation phenomena similar to those in discontinuous equilibrium transitions.
Skip Nav Destination
Article navigation
21 February 2009
Research Article|
February 19 2009
Schloegl’s second model for autocatalysis with particle diffusion: Lattice-gas realization exhibiting generic two-phase coexistence
Xiaofang Guo;
Xiaofang Guo
1Ames Laboratory, USDOE,
Iowa State University
, Ames, Iowa 50011, USA
2Department of Physics and Astronomy,
Iowa State University
, Ames, Iowa 50011, USA
3Department of Mathematics,
Iowa State University
, Ames, Iowa 50011, USA
Search for other works by this author on:
Da-Jiang Liu;
Da-Jiang Liu
1Ames Laboratory, USDOE,
Iowa State University
, Ames, Iowa 50011, USA
Search for other works by this author on:
J. W. Evans
J. W. Evans
a)
1Ames Laboratory, USDOE,
Iowa State University
, Ames, Iowa 50011, USA
3Department of Mathematics,
Iowa State University
, Ames, Iowa 50011, USA
Search for other works by this author on:
a)
Electronic mail: evans@ameslab.gov.
J. Chem. Phys. 130, 074106 (2009)
Article history
Received:
October 04 2008
Accepted:
January 05 2009
Citation
Xiaofang Guo, Da-Jiang Liu, J. W. Evans; Schloegl’s second model for autocatalysis with particle diffusion: Lattice-gas realization exhibiting generic two-phase coexistence. J. Chem. Phys. 21 February 2009; 130 (7): 074106. https://doi.org/10.1063/1.3074308
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
DeePMD-kit v2: A software package for deep potential models
Jinzhe Zeng, Duo Zhang, et al.
CREST—A program for the exploration of low-energy molecular chemical space
Philipp Pracht, Stefan Grimme, et al.
Related Content
Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability
J. Chem. Phys. (April 2015)
Kinetics of autocatalysis in small systems
J. Chem. Phys. (January 2008)
Necessary conditions for the emergence of homochirality via autocatalytic self-replication
J. Chem. Phys. (August 2016)
Symmetry Breaking in Asymmetric Autocatalysis of Pyrimidyl Alkanol
AIP Conference Proceedings (March 2008)
Chiral symmetry breaking in a microscopic model with asymmetric autocatalysis and inhibition
J. Chem. Phys. (December 2010)