Eisenbud and Harris introduced the theory of limit linear series, and constructed a space parametrizing their limit linear series. Recently, Osserman introduced a new space which compactifies the Eisenbud-Harris construction. In the Eisenbud-Harris space, the set of refined limit linear series is always dense on a general reducible curve. Osserman asks when the same is true for his space. In th...

The Harris-Luck criterion judges the relevance of ~potentially! spatially correlated, quenched disorder induced by, e.g., random bonds, randomly diluted sites, or a quasiperiodicity of the lattice, for altering the critical behavior of a coupled matter system. We investigate the applicability of this type of criterion to the case of spin variables coupled to random lattices. Their aptitude to a...