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arXiv · 2006.14533

On the monotonicity of the critical time in the Constrained-degree percolation model

Charles S. do Amaral·A. P. F. Atman·Bernardo N. B. de Lima
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Abstract

The Constrained-degree percolation model was introduced in [B.N.B. de Lima, R. Sanchis, D.C. dos Santos, V. Sidoravicius, and R. Teodoro, Stoch. Process. Appl. (2020)], where it was proven that this model has a non-trivial phase transition on a square lattice. We study the Constrained-degree percolation model on the $d$-dimensional hypercubic lattice ($\mathbb{Z}^d$) and, via numerical simulations, found evidence that the critical time $t_{c}^{d}(k)$ is monotonous not increasing in the constrained $k$ if $d=3,4$, like it is when $d=2$. We verify that the lowest constrained value $k$ such that the system exhibits a phase transition is $k=3$ and that the correlation critical exponent $ν$ for the Constrained-degree percolation model and ordinary Bernoulli percolation are the same.

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Charles S. do Amaral, A. P. F. Atman, Bernardo N. B. de Lima. 2020-09-19. On the monotonicity of the critical time in the Constrained-degree percolation model. https://doi.org/10.1016/j.physa.2020.125291

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