Nonequilibrium phase transition of a one dimensional system reaches the absorbing state by two different ways

Abstract

Abstract We study the nonequilibrium phase transitions from the absorbing phase to the active phase for the model of diseases spreading (Susceptible-Infected-Refractory-Susceptible (SIRS)) on a regular one-dimensional lattice. In this model, particles of three species (S, I, and R) on a lattice react as follows: $$S+I\rightarrow 2I$$ S + I → 2 I with probability $$\lambda $$ λ , $$I\rightarrow R$$ I → R after infection time $$\tau _I$$ τ I and $$R\rightarrow I$$ R → I after recovery time $$\tau _R$$ τ R . In the case of $$\tau _R>\tau _I$$ τ R > τ I , this model has been found to have two critical thresholds separating the active phase from absorbing phases. The first critical threshold $$\lambda _{c1}$$ λ c 1 corresponds to a low infection probability and the second critical threshold $$\lambda _{c2}$$ λ c 2 corresponds to a high infection probability. At the first critical threshold $$\lambda _{c1}$$ λ c 1 , our Monte Carlo simulations of this model suggest the phase transition to be of directed percolation class (DP). However, at the second critical threshold $$\lambda _{c2}$$ λ c 2 we observe that the system becomes so sensitive to initial values conditions which suggest the phase transition to be a discontinuous transition. We confirm this result using order parameter quasistationary probability distribution and finite-size analysis for this model at $$\lambda _{c2}$$ λ c 2 .