On two classes of nearly binary matroids

We give an excluded-minor characterization for the class of matroids M in which M\e or M/e is binary for all e in E(M). This class is closely related to the class of matroids in which every member is binary or can be obtained from a binary matroid by relaxing a circuit-hyperplane. We also provide an excluded-minor characterization for the second class.Comment: 14 pages, 4 figures. This paper has been accepted for publication in the European Journal of Combinatorics. This is the final version of the pape

Quantum Impurity in a Nearly Critical Two Dimensional Antiferromagnet

We describe the spin dynamics of an arbitrary localized impurity in an insulating two dimensional antiferromagnet, across the host transition from a paramagnet with a spin gap to a Neel state. The impurity spin susceptibility has a Curie-like divergence at the quantum-critical coupling, but with a universal, effective spin which is neither an integer nor a half-odd-integer. In the Neel state, the transverse impurity susceptibility is a universal number divided by the host spin stiffness (which determines the energy cost to slow twists in the orientation of the Neel order). These, and numerous other results for the thermodynamics, Knight shift, and magnon damping have significant applications to experiments on layered transition metal oxides.Comment: 12 pages, 3 figures; Additional details and results are in cond-mat/991202