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We study the effect of dilute pinning on the jamming transition. Pinning reduces the average contact number needed to jam unpinned particles and shifts the jamming threshold to lower densities, leading to a pinning susceptibility, χp. Our main results are that this susceptibility obeys scaling form and diverges in the thermodynamic limit as χp∝|ϕ−ϕ∞c|−γp where ϕ∞c is the jamming threshold in the absence of pins. Finite-size scaling arguments yield these values with associated statistical (systematic) errors γp=1.018±0.026(0.291) in d=2 and γp=1.534±0.120(0.822) in d=3. Logarithmic corrections raise the exponent in d=2 to close to the d=3 value, although the systematic errors are very large. [ABSTRACT FROM AUTHOR]

We construct ferroelectric (LuFeO_{3})_{m}/(LuFe_{2}O_{4}) superlattices with varying index m to study the effect of confinement on topological defects. We observe a thickness-dependent transition from neutral to charged domain walls and the emergence of fractional vortices. In thin LuFeO_{3} layers, the volume fraction of domain walls grows, lowering the symmetry from P6_{3}cm to P3c1 before reaching the nonpolar P6_{3}/mmc state, analogous to the group-subgroup sequence observed at the high-temperature ferroelectric to paraelectric transition. Our study shows how dimensional confinement stabilizes textures beyond those in bulk ferroelectric systems.