The symbiotic contact process: phase transitions, hysteresis cycles, and bistability

Abstract

We performed Monte Carlo simulations of the symbiotic contact process on different spatial dimensions ($d$). On the complete and random graphs (infinite dimension), we observe hysteresis cycles and bistable regions, what is consistent with the discontinuous absorbing-state phase transition predicted by mean-field theory. By contrast, on a regular square lattice, we find no signs of bistability or hysteretic behavior. This result suggests that the transition in two dimensions is rather continuous. Based on our numerical observations, we conjecture that the nature of the transition changes at the upper critical dimension ($d_c$), from continuous ($d<d_c$) to discontinuous ($d>d_c$).

arXiv comment6 pages, 6 figures

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Cited by in corpus (5)

• A simple mechanism leading to first-order phase transitions in a model of tax evasion
• Heterogeneous mean-field theory for two-species symbiotic processes on networks
• Tricritical behavior in epidemic dynamics with vaccination
• Dynamical correlations and pairwise theory for the symbiotic contact process on networks
• Visibility graphs of critical and off-critical time series for absorbing state phase transitions