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Zeitschrift für Physik B Condensed Matter

, Volume 47, Issue 4, pp 365–374 | Cite as

On phase transitions in Schlögl's second model

  • P. Grassberger
Article

Abstract

We study Schlögl's second model, characterized by chemical reactions
$$\begin{array}{*{20}c} {2X\underset{{k_2 }}{\overset{{k_1 }}{\longleftrightarrow}}3X,} & {X\underset{{k_4 }}{\overset{{k_3 }}{\longleftrightarrow}}0,} \\ \end{array} $$
ind-dimensional space. The reactions are assumed to be local; local fluctuations are fully taken into account, and particle transport occurs via diffusion.

In contrast to previous investigations, we find no phase transition whenk4≠0 andd<4. Fork4=0,k3≠0, and 1≦d<4, we find a second-order phase transition which is in the same universality class as the transition in Schlögl's first model. Only ford≧4 we do find the first-order transition found also by previous authors.

These claims are supported by extensive Monte Carlo calculations for various realizations of this process on discrete space-time lattices.

Keywords

Spectroscopy Neural Network Phase Transition State Physics Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • P. Grassberger
    • 1
  1. 1.Physik Department der UniversitätWuppertalFederal Republic of Germany

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