Abstract
A two-dimensional atomistic realization of Schlögl’s second model for autocatalysis is implemented and studied on a square lattice as a prototypical nonequilibrium model with first-order transition. The model has no explicit symmetry and its phase transition can be viewed as the nonequilibrium counterpart of liquid-vapor phase separations. We show some familiar concepts from study of equilibrium systems need to be modified. Most importantly, phase coexistence can be a generic feature of the model, occurring over a finite region of the parameter space. The first-order transition becomes continuous as a temperature-like variable increases. The associated critical behavior is studied through Monte Carlo simulations and shown to be in the two-dimensional Ising universality class. However, some common expectations regarding finite-size corrections and fractal properties of geometric clusters for equilibrium systems seems to be inapplicable.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Marro, J., Dickman, R.: Nonequilibrium Phase Transitions in Lattice Models. Cambridge University Press, Cambridge, (1999)
Hinrichsen, H.: Adv. Phys. 49, 815 (2000)
Ódor, G.: Rev. Mod. Phys. 76, 663 (2004)
Grinstein, G., Yayaprakash, C., He, Y.: Phys. Rev. Lett. 55, 2527 (1985)
de Oliveira, M.J., Mendes, J.F.F., Santos, M.A.: J. Phys. A 26, 2317 (1993)
Tomé, T., Dickman, R.: Phys. Rev. E 47, 948 (1993)
Liu, D.J., Pavlenko, N., Evans, J.W.: J. Stat. Phys. 114, 101 (2004)
Machado, E., Buendía, G.M., Rikvold, P.A., Ziff, R.M.: Phys. Rev. E 71, 016120 (2005)
Liu, D.J., Evans, J.W.: J. Chem. Phys. 117, 7319 (2002)
Machado, E., Buendıa, G.M., Rikvold, P.A.: Phys. Rev. E 71, 031603 (2005)
Durrett, R.: SIAM Rev. 41, 677 (1999)
Liu, D.J., Guo, X., Evans, J.W.: Phys. Rev. Lett. 98, 050601 (2007)
Guo, X., Liu, D.J., Evans, J.W.: Phys. Rev. E 75, 061129 (2007)
Guo, X., Evans, J.W., Liu, D.J.: Physica A 387, 177 (2008)
Schlögl, F.: Z. Phys. 253, 147 (1972)
Brosilow, B.J., Ziff, R.M.: Phys. Rev. A 46, 4534 (1992)
Toom, A.L.: In: Dobrushin, R.L., Sinai, Y.G. (eds.) Multicomponent Random Systems. Advances in Probability and Related Topics, vol. 6, pp. 549–575. Dekker, New York (1980), Chap. 18
Bennett, C.H., Grinstein, G.: Phys. Rev. Lett. 55, 657 (1985)
Muñoz, M.A., de los Santos, F., da Gama, M.M.T.: Eur. Phys. J. B 43, 73 (2005)
Hinrichsen, H., Livi, R., Mukamel, D., Politi, A.: Phys. Rev. E 61, R1032 (2000)
Drouffe, J.M., Godréche, C.: J. Phys. A 32, 249 (1999)
Ziff, R.M., Gulari, E., Barshad, Y.: Phys. Rev. Lett. 56(24), 2553 (1986)
Orkoulas, G., Fisher, M.E., Panagiotopoulos, A.Z.: Phys. Rev. E 63, 051507 (2001)
Coniglio, A., Klein, W.: J. Phys. A 13, 2775 (1980)
Stella, A.L., Vanderzande, C.: Phys. Rev. Lett. 62, 1067 (1989)
Hu, C.K., Mak, K.S.: Phys. Rev. B 39, 2948 (1989)
Liu, D.J., Evans, J.W.: Phys. Rev. Lett. 84, 955 (2000)
Liu, D.J., Evans, J.W.: Phys. Rev. B 62, 2134 (2000)
Fortunato, S.: Phys. Rev. B 67, 014102 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, DJ. Generic Two-Phase Coexistence and Nonequilibrium Criticality in a Lattice Version of Schlögl’s Second Model for Autocatalysis. J Stat Phys 135, 77–85 (2009). https://doi.org/10.1007/s10955-009-9708-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-009-9708-2