We present specific heat data on the system Fe p Zn 1- p L 6(ClO 4) 2, which is an experimental realization of the sc, S = 1 2 , diluted Ising antiferromagnet. Here L = C 5 H 5 NO. The results are compared with earlier data on the diluted sc, S = 1 2 , XY antiferromagnet Co p Zn 1- p L 6(Cl) 4) 2 and the diluted bcc, S = 1 2 , Ising antiferromagnet Co p Zn 1- p Cs 3Cl 5. The specific heat behaviour of the diluted Ising systems is found to be completely different from that of the diluted XY magnet, for which very strong short-range order effects have been observed. An explanation is given in terms of the fractal properties of the infinite percolation cluster in the temperature range above T c( p). It is shown that there exists a strong analogy between the specific heat behaviour of a diluted magnet and that of a system of weakly coupled magnetic chains. In this picture a decrease of p corresponds with a decrease of the coupling between the chains. The differences in behaviour observed between the Ising systems on the one hand, and the (isotropic) XY or Heisenberg systems on the other, can then be explained by the fact that the intrachain correlation length depends exponentially on temperature for the Ising chain, whereas it depends much less strongly on temperature (∝ 1/ T) for the XY and Heisenberg chains.