Abstract.
Microscopic modeling of complex systems by cellular automata, which deal with particles at lattice sites interacting via simple local rules, involves some arbitrariness besides a drastic simplification of nature. Here we briefly report on some recent work on the influence of dynamic details on the morphological and critical properties of one of such model systems. In particular, we discuss on the similarities and differences between a kinetic nonequilibrium Ising model—which is a prototype for nonequilibrium anisotropic phase transitions—and its off–lattice counterpart, namely, an analogue in which the spatial coordinates of the particles vary continuously. We also pay attention to a related driven lattice model with nearest-neighbor exclusion.
Similar content being viewed by others
References
B. Chopard, M. Droz, Cellular Automata Modeling of Physical Systems (Cambridge University Press, Cambridge, UK, 1998)
J. Marro, R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, UK, 1999)
S. Katz, J.L. Lebowitz, H. Spohn, Phys. Rev. B 28, 1655 (1983); ibid, J. Stat. Phys. 34, 497 (1984)
B. Schmittmann, R.K.P. Zia, in Statistical Mechanics of Driven Diffusive Systems, in Phase Transitions and Critical Phenomena (Academic, London, UK, 1996)
A. Achahbar, P.L. Garrido, J. Marro, M.A. Muñoz, Phys. Rev. Lett. 87, 195702 (2001)
M. Díez–Minguito, P.L. Garrido, J. Marro, Phys. Rev. E 72, 026103 (2005)
J. Marro, P.L. Garrido, M. Díez–Minguito, Phys. Rev. B 73, 184115 (2006)
M.P. Allen, D.J. Tidlesley, Computer Simulations of Liquids (Oxford University Press, Oxford, UK 1987)
A.D. Rutenberg, C. Yeung, Phys. Rev. E 60, 2710 (1999)
P.I. Hurtado et al., Phys. Rev. B 67, 014206 (2003)
T.M. Squiresa, S.R. Quake, Rev. Mod. Phys. 77, 977 (2005)
M. Díez–Minguito et al. (to be published)
A. Szolnoki, G. Szabó, Phys. Rev. E 65, 047101 (2002)
R. Dickman, Phys. Rev. E 64, 016124 (2001)
K.J. Strandburg, Rev. Mod. Phys. 60, 161 (1988)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Díez-Minguito, M., Marro, J. & Garrido, P. On the similarities and differences between lattice and off–lattice models of driven fluids. Eur. Phys. J. Spec. Top. 143, 269–272 (2007). https://doi.org/10.1140/epjst/e2007-00101-4
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2007-00101-4