Loop soup percolation on Z^d, d≥5, has discrete threshold strictly above the cable system threshold 1/2; on trees, Poisson zoo percolation and susceptibility thresholds coincide, and the model is infinitesimally sensitive to Bernoulli enhancement.
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(Non-)coincidence of critical parameters for Poisson Zoos and Loop Soup Percolation on $\mathbb{Z^d}$, $d > 4$, and $\mathbb{T}_d$,$ d \ge 3$
Loop soup percolation on Z^d, d≥5, has discrete threshold strictly above the cable system threshold 1/2; on trees, Poisson zoo percolation and susceptibility thresholds coincide, and the model is infinitesimally sensitive to Bernoulli enhancement.