One-dimensional Absorbing phase transition in the fermionic parity-conserving particle process with second neighbors branching

Abstract

By means of Monte Carlo procedure this article analyzes a stochastic process in one-dimensional model. The parity-conserving particle process with infinite annihilation and branching of the two offspring to the second neighbors, each one at each side. The model was firstly considered in Takayasu and Tretyakov (1991) and Jensen (1994) but branching of four offspring to four first neighbors. It has also been solved in Zhong and ben-Avraham (1995) with branching of the two particles to the first neighbors, each one at each side, but with finite annihilation. Now the model has been studied with infinite annihilation in presence of only second neighbors branching of two particles, one to left and the other to the right. Simulations were performed on a regular one dimension lattice in order to determine the threshold of absorbing phase transition. From steady state simulations and finite time scaling analysis, it is shown that the transition exists and critical exponents are obtained. The exponents are found to differ from those of the directed percolation (DP) universality class and are the same found in Takayasu and Tretyakov (1991), Jensen (1994) and Zhong and ben-Avraham (1995). It is also calculated the short-time relaxation dynamical critical exponents and checked the consistence of the related scaling relation.