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Within the $t$-$J$ model, we study the doping dependence ofantiferromagnetism in the copper oxide materials by considering quantumfluctuations of spinons in the random-phase-approximation. The staggeredmagnetization vanishes around doping $\delta=5%$ for a reasonable parametervalue $t/J=5$, which is in agreement with the experiments on copper oxidematerials.Comment: 14 page

ESTIMATION OF THE DOPING DEPENDENCE OF ANTIFERROMAGNETISM IN THE COPPER OXIDE MATERIAL