Smoothly vanishing density in the contact process by an interplay of disorder and long-distance dispersal
arxiv(2024)
Abstract
Realistic modeling of ecological population dynamics requires spatially
explicit descriptions that can take into account spatial heterogeneity as well
as long-distance dispersal. Here, we present Monte Carlo simulations and
numerical renormalization group results for the paradigmatic model, the contact
process, in the combined presence of these factors in both one and
two-dimensional systems. Our results confirm our analytic arguments stating
that the density vanishes smoothly at the extinction threshold, in a way
characteristic of infinite-order transitions. This extremely smooth vanishing
of the global density entails an enhanced exposure of the population to
extinction events. At the same time, a reverse order parameter, the local
persistence displays a discontinuity characteristic of mixed-order transitions,
as it approaches a non-universal critical value algebraically with an exponent
β_p'<1.
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