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On the absorbing-state phase transition in the one-dimensional triplet creation model. (English) Zbl 1459.82214

Summary: We study the lattice reaction-diffusion model \(3 \text{A}\to 4 \text{A} , \text{A}\to \emptyset \) (“triplet creation”) using numerical simulations and \(n\)-site approximations. The simulation results suggest that the phase transition is discontinuous at high diffusion rates. In this regime the order parameter appears to be a discontinuous function of the creation rate; no evidence of a stable interface between active and absorbing phases is found. Based on an effective mapping to a modified compact directed percolation process, we shall nevertheless argue that the transition is continuous, despite the seemingly discontinuous phase transition suggested by studies of finite systems.

MSC:

82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
82-10 Mathematical modeling or simulation for problems pertaining to statistical mechanics
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