Phase transition classes in triplet and quadruplet reaction diffusion models

Details Phase transition classes in triplet and quadruplet reaction diffusion models Phase transition classes in triplet and quadruplet reaction diffusion models

2002-10-28

arxiv.org/abs/cond-mat/0210615v2

Phys. Rev. E 67 (2003) 056114.

Physics

Condensed Matter

Statistical Mechanics

8 pages, 10 figures included, Updated with new data, figures, table, to be published in PRE

Scientific paper

10.1103/PhysRevE.67.056114

Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n=3,4 parents, whereas explicit diffusion of single particles (A) is present are investigated in low dimensions by mean-field approximation and simulations. The mean-field approximation of general nA -> (n+k)A, mA -> (m-l)A type of lattice models is solved and novel kind of critical behavior is pointed out. In d=2 dimensions the 3A -> 4A, 3A -> 2A model exhibits a continuous mean-field type of phase transition, that implies d_c<2 upper critical dimension. For this model in d=1 extensive simulations support a mean-field type of phase transition with logarithmic corrections unlike the Park et al.'s recent study (Phys. Rev E {\bf 66}, 025101 (2002)). On the other hand the 4A -> 5A, 4A -> 3A quadruplet model exhibits a mean-field type of phase transition with logarithmic corrections in d=2, while quadruplet models in 1d show robust, non-trivial transitions suggesting d_c=2. Furthermore I show that a parity conserving model 3A -> 5A, 2A->0 in d=1 has a continuous phase transition with novel kind of exponents. These results are in contradiction with the recently suggested implications of a phenomenological, multiplicative noise Langevin equation approach and with the simulations on suppressed bosonic systems by Kockelkoren and Chat\'e (cond-mat/0208497).

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