Planar and Stripe Orders of Doped Mott Insulators In Dual Spin Models

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We focus on very general, very large U, doped Mott Insulators with arbitrary hopping and interactions. We provide simple testimony to the competition between magnetic and superconducting orders in these systems. By mapping hard core bosons, spinless, and spinful fermions onto XXZ models, we aim to make very simple precise statements. We try to address optimal and expected filling fractions of holes within the plane and on stripes in a variety of hole and hole pair geometries. We examine the role of attractions/repulsion amongst hole pairs and single holes, and provide trivial expected numerical values for filling fractions in various scenarios. We demnostrate that plaquette states seem to naturally provide the correct stripe filling fractions.