The solutions of the site percolation problem for some Bethe lattices of interacting spins are shown. For zero external field some arguments are given which predict for three-dimensional models p c < 1 / 2 and for planar models p c = 1 / 2 where p c is the critical density of overturned spins for the percolation problem.
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Antonio Coniglio (1975) studied this question.
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