Phase transition classes in triplet and quadruplet reaction-diffusion models.

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 the 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 a different 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 recent study of Park et al. [Phys. Rev E 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 one-dimensional show robust, nontrivial transitions suggesting d(c)=2. Furthermore, I show that a parity conserving model 3A-->5A, 2A--> zero in d=1 has a continuous phase transition with different kinds 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 Chaté [Phys. Rev. Lett. 90, 125701 (2003)].