Phase diagram of a stochastic cellular automaton with long-range interactions

Sergio A. Cannas

Physica A: Statistical Mechanics and its Applications, 1998, vol. 258, issue 1, 32-44

Abstract: A stochastic one-dimensional cellular automaton with long range spatial interactions is introduced. In this model the state probability of a given site at time t depends on the state of all the other sites at time t−1 through a power law of the type 1/rα, r being the distance between sites. For α→∞ this model reduces to the Domany–Kinzel cellular automaton. The dynamical phase diagram is analyzed using Monte Carlo simulations for 0⩽α⩽∞. We found the existence of two different regimes: one for 0⩽α⩽1 and the other for α>1. It is shown that in the first regime the phase diagram becomes independent of α. Regarding the frozen-active phase transition in this regime, a strong evidence is found that the mean-field prediction for this model becomes exact, a result already encountered in magnetic systems. It is also shown that, for replicas evolving under the same noise, the long-range interactions fully suppress the spreading of damage for 0⩽α⩽1.

Keywords: Cellular automata; Long-range interactions; Phase transitions; Spreading of damage (search for similar items in EconPapers)
Date: 1998
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437198002702
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:258:y:1998:i:1:p:32-44

DOI: 10.1016/S0378-4371(98)00270-2

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().