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Site Percolation Thresholds of FCC Lattice

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Percolation thresholds, p_{c}, for site diluted spin systems on the fcc lattice are determined for exchange interactions extending up to the shell of the fourth nearest neighbors. If the interactions include the nearest, second, third, and fourth neighbors, p_{c} is equal to 0.198, 0.136, 0.061, and 0.05 respectively. These results agree with the Roberts approximate formula for p_{c}. Estimation of p_{c} to even longer-ranged couplings is presented. For instance for p_{c} = 0.01 the range of the couplings should extend at least to the eight shell of neighbors.
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