Nonequilibrium phase transition of a one dimensional system reaches the absorbing state by two different ways
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We study the nonequilibrium phase transitions from the absorbing phase to the active phase for the model of disease 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→ 2I with probability λ, I→ R after infection time τ_I and R→ I after recovery time τ_R. In the case of τ_R>τ_I, this model has been found to has two critical thresholds separate the active phase from absorbing phases <cit.>. The first critical threshold λ_c1 is corresponding to a low infection probability and second critical threshold λ_c2 is corresponding to a high infection probability. At the first critical threshold λ_c1, our Monte Carlo simulations of this model suggest the phase transition to be of directed percolation class (DP). However, at the second critical threshold λ_c2 we observe that, the system becomes so sensitive to initial values conditions which suggests the phase transition to be discontinuous transition. We confirm this result using order parameter quasistationary probability distribution and finite-size analysis for this model at λ_c2. Additionally, the typical space-time evolution of this model at λ_c2 shows that, the spreading of active particles are compact in a behavior which remind us the spreading behavior in the compact directed percolation.14
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