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Influence of competition in minimal systems with discontinuous absorbing phase transitions

Contact processes (CP's) with particle creation requiring a minimal neighborhood (restrictive or threshold CP's) present a novel sort of discontinuous absorbing transitions, that revealed itself robust under the inclusion of different ingredients, such as distinct lattice topologies, particle annihilations and diffusion. Here, we tackle on the influence of competition between restrictive and standard dynamics (that describes the usual CP and a continuous DP transition is presented). Systems have been studied via mean-field theory (MFT) and numerical simulations. Results show partial contrast between MFT and numerical results. While the former predicts that considerable competition rates are required to shift the phase transition, the latter reveals the change occurs for rather limited (small) fractions. Thus, unlike previous ingredients (such as diffusion and others), limited competitive rates suppress the phase coexistence.