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Phase diagrams in the plane of $r_A$ (the average ionic radius, related toone-electron bandwidth $W$) and $\sigma^2$ (the ionic radius variance,measuring the quenched disorder), or ``bandwidth-disorder phase diagrams'',have been established for perovskite manganites, with three-dimensional (3$D$)Mn-O network. Here we establish the intrinsic bandwidth-disorder phase diagramof half-doped layered manganites with the two-dimensional (2$D$) Mn-O network,examining in detail the ``mother state'' of the colossal magnetoresistance(CMR) phenomenon in crystals without ferromagnetic instability. Theconsequences of the reduced dimensionality, from 3$D$ to 2$D$, on theorder-disorder phenomena in the charge-orbital sectors are also highlighted.Comment: REVTeX 4 style; 5 pages, 4 figure

Bandwidth-disorder phase diagram of half-doped layered manganites