Phase transition classes in triplet and quadruplet reaction diffusion models

TL;DR

This paper investigates phase transitions in reaction-diffusion models with triplet and quadruplet particle creation, revealing novel critical behaviors, mean-field type transitions, and challenging previous theoretical predictions.

Contribution

It introduces new classes of reaction-diffusion models with n=3,4 parent particle creation, analyzing their phase transitions through mean-field and simulation methods, and uncovers unexpected critical behaviors.

Findings

3A -> 4A, 3A -> 2A model shows mean-field transition in 2D

Quadruplet models exhibit mean-field transition with corrections in 2D

1D models display non-trivial transitions, challenging previous theories

Abstract

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).