On phase transitions in Schlögl's second model

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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 whenk 4≠0 andd<4. Fork 4=0,k 3≠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.

Address from April 1-September 30, 1982: Chemical Physics Department, Weizmann Institute of Science, Rehovot, Israel