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We make a new proposal to describe the very low temperature susceptibility ofthe doped Haldane gap compound Y$_2$BaNi$_{1-x}$Zn$_x$O$_5$. We propose a newmean field model relevant for this compound. The ground state of this meanfield model is unconventional because antiferromagnetism coexists with randomdimers. We present new susceptibility experiments at very low temperature. Weobtain a Curie-Weiss susceptibility $\chi(T) \sim C / (\Theta+T)$ as expectedfor antiferromagnetic correlations but we do not obtain a direct signature ofantiferromagnetic long range order. We explain how to obtain the ``impurity''susceptibility $\chi_{imp}(T)$ by subtracting the Haldane gap contribution tothe total susceptibility. In the temperature range [1 K, 300 K] theexperimental data are well fitted by $T \chi_{imp}(T) = C_{imp} (1 + T_{imp}/T)^{-\gamma}$. In the temperature range [100 mK, 1 K] the experimental data arewell fitted by $T \chi_{imp}(T) = A \ln{(T/T_c)}$, where $T_c$ increases with$x$. This fit suggests the existence of a finite N\'eel temperature which ishowever too small to be probed directly in our experiments. We also obtain amaximum in the temperature dependence of the ac-susceptibility $\chi'(T)$ whichsuggests the existence of antiferromagnetic correlations at very lowtemperature.Comment: 19 pages, 17 figures, revised version (minor modifications

Unconventional antiferromagnetic correlations of the doped Haldane gapsystem Y 2 BaNi 1 - x Zn x O 5