Non-analytic magnetic field dependence of quasi-particle properties of two-dimensional metals

We show that in a weak external magnetic field H the quasi-particle residue and the renormalized electron Lande factor of two-dimensional Fermi liquids exhibit a non-analytic magnetic field dependence proportional to |H| which is due to electron-electron interactions. We explicitly calculate the corresponding prefactors to second order in the interaction and show that they are determined by low-energy scattering processes involving only momenta close to the Fermi surface. Experimentally, these non-analytic terms can be detected from measurements of the magnetic field dependence of the density of states and the magnetoconductivity.Comment: 11 pages, 5 figure

Box complexes, neighborhood complexes, and the chromatic number

Lovasz's striking proof of Kneser's conjecture from 1978 using the Borsuk--Ulam theorem provides a lower bound on the chromatic number of a graph. We introduce the shore subdivision of simplicial complexes and use it to show an upper bound to this topological lower bound and to construct a strong Z_2-deformation retraction from the box complex (in the version introduced by Matousek and Ziegler) to the Lovasz complex. In the process, we analyze and clarify the combinatorics of the complexes involved and link their structure via several ``intermediate'' complexes.Comment: 8 pages, 1 figur