Abstract
It is argued that near the percolation threshold of diluted systems there should be an instability of the long-range order in spatially random fields much smaller than the local molecular fields as a result of the strong ramification of the infinite percolation cluster, in all dimensions. This may give a possible explanation for the experiments of Yoshizawa et al., who find a destruction of the long-range order due to relatively small external magnetic fields in diluted two- and three-dimensional Ising antiferromagnets.
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