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Spin models that have been proposed to describe dimerized chains, ladders,two dimensional antiferromagnets, and other compounds are here studied whensome spins are replaced by spinless vacancies, such as it occurs by $Zn$doping. A small percentage of vacancies rapidly destroys the spin gap, andtheir presence induces enhanced antiferromagnetic correlations near thosevacancies. The study is performed with computational techniques which includesLanczos, world-line Monte Carlo, and the Density Matrix Renormalization Groupmethods. Since the phenomenon of enhanced antiferromagnetism is found to occurin several models and cluster geometries, a common simple explanation for itspresence may exist. It is argued that the resonating-valence-bond character ofthe spin correlations at short distances of a large variety of models isresponsible for the presence of robust staggered spin correlations nearvacancies and lattice edges. The phenomenon takes place regardless of the longdistance properties of the ground state, and it is caused by a ``pruning'' ofthe available spin singlets in the vicinity of the vacancies. The effectproduces a broadening of the low temperature NMR signal for the compoundsanalyzed here. This broadening should be experimentally observable in thestructurally dimerized chain systems  $Cu(NO_3)_2\cdot2.5H_2O$, $CuWO_4$, $(VO)_2P_2O_7$, and$Sr_{14}Cu_{24}O_{41}$, in ladder materials such as $Sr Cu_2 O_3$, in thespin-Peierls systems $CuGeO_3$ and $NaV_2 O_5$, and in several others since itis a universal effect common to a wide variety of models and compounds.Comment: 18 pages revtex with 26 figures include

Enhancement of antiferromagnetic correlations induced by nonmagnetic impurities: Origin and predictions for NMR experiments