On phase transitions in Schlögl's second model

Abstract

We study Schlögl's second model, characterized by chemical reactions {Mathematical expression} in d-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 when k 4 ≠0 and d<4. For k 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 for d≧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. © 1982 Springer-Verlag.