Effect of diffusion in simple discontinuous absorbing transition models

Abstract

Discontinuous transitions into absorbing states require an effective mechanism that prevents the stabilization of low density states. They can be found in different systems, such as lattice models or stochastic differential equations (e.g. Langevin equations). Recent results for the latter approach have shown that the inclusion of limited diffusion suppresses discontinuous transitions, whereas they are maintained for larger diffusion strengths. Here we give a further step by addressing the effect of diffusion in two simple lattice models originally presenting discontinuous absorbing transitions. They have been studied via mean-field theory (MFT) and distinct sort of numerical simulations. For both cases, results suggest that the diffusion does not change the order of the transition, regardless its strength and thus, in partial contrast with results obtained from Langevin approach. Also, all transitions present a common finite size scaling behavior that is similar to discontinuous absorbing transitions studied in Phys. Rev. E 89, 022104 (2014).

Influence of competition in minimal systems with discontinuous absorbing phase transitions

“…Results showed that limited competition rates are sufficient for the suppression of phase coexistence. This is in partial contrast with previous results [18,20] like particle diffusion and distinct annihilation rules do not shift the discontinuous transitions. As a final comment, we mention that all results for the first-order transitions reinforce previous claims over a common finite-size scaling for nonequilibrium transitions [18,20,21], in which in similarity with the equilibrium case, relevant quantities scale with the system volume.…”

“…For equilibrium systems, the maximum of χ and other quantities scale with the system volume and its position α L obeys the asymptotic relation α L = α 0 − c/L 2 [24,25], being α 0 the transition point in the thermodynamic limit and c a constant. Recent papers [18,26,20,21] have shown that similar scaling is verified for nonequilibrium phase transitions. Alternatively, the transition point can also be estimated as the value of α L in which the two peaks of the probability distribution have equal weights (area) [26,21].…”

“…In order to enhance the understanding about the robustness of discontinuous absorbing phase transitions presented in such simple (minimal) models, here we extend the study undertaken in Ref. [20] by addressing the competition between the above restrictive and standard dynamics (that describes the usual CP). In the last case, the transition belongs to the usual and robust directed percolation (DP) universality class.…”

“…Different restrictive models have revealed that the phase transition remains first-order by including other sorts of creation [9,15,16,17,18], annihilation rules [18] and also different lattice topologies [19]. Besides, a very recent study [20] has claimed that the particle diffusion does not suppress the phase coexistence, in partial contrast with results obtained from stochastic differential equation approaches [10].…”

Competition between dynamic ordering and disordering for vortices driven by superimposed ac and dc forces

“…To obtain stronger evidence for our view mentioned in this work and deeper insight into the phenomena, further experiments, such as exploring direct visualization of the vortex configuration [52,59], as well as theoretical investigation, may be needed. We believe that the present study will stimulate similar experiments and analysis in other systems where the dynamic ordering and disordering would be observed [10,16,41,48,[60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75].…”