Fractional impurity moments in two-dimensional non-collinear magnets

We study dilute magnetic impurities and vacancies in two-dimensional frustrated magnets with non-collinear order. Taking the triangular-lattice Heisenberg model as an example, we use quasiclassical methods to determine the impurity contributions to the magnetization and susceptibility. Most importantly, each impurity moment is not quantized, but receives non-universal screening corrections due to local relief of frustration. At finite temperatures, where bulk long-range order is absent, this implies an impurity-induced magnetic response of Curie form, with a prefactor corresponding to a fractional moment per impurity. We also discuss the behavior in an applied magnetic field, where we find a singular linear-response limit for overcompensated impurities, and propose experiments to test our theory.Comment: 4 pages, 4 fig

On the Koplienko spectral shift function, I. Basics

We study the Koplienko Spectral Shift Function (KoSSF), which is distinct from the one of Krein (KrSSF). KoSSF is defined for pairs $A,B$ with (A-B)\in\calI_2, the Hilbert-Schmidt operators, while KrSSF is defined for pairs $A,B$ with (A-B)\in\calI_1, the trace class operators. We review various aspects of the construction of both KoSSF and KrSSF. Among our new results are: (i) that any positive Riemann integrable function of compact support occurs as a KoSSF; (ii) that there exist $A,B$ with (A-B)\in\calI_2 so $\det_2((A-z)(B-z)^{-1})$ does not have nontangential boundary values; (iii) an alternative definition of KoSSF in the unitary case; and (iv) a new proof of the invariance of the a.c. spectrum under \calI_1-perturbations that uses the KrSSF.Comment: Submitted to the Marchenko and Pastur birthday issue of Journal of Mathematical Physics, Analysis and Geometr

Mass dependent Evolution of Field Early-Type Galaxies Since z=1

We present the Fundamental Plane (FP) of field early-type galaxies at 0.5<z<1.0. Our project is a continuation of our efforts to understand the formation and evolution of early-type galaxies in different environments. The target galaxies were selected from the comprehensive and homogeneous data set of the Gemini/HST Galaxy Cluster Project. The distant field early-type galaxies follow a steeper FP relation compared to the local FP. The change in the slope of the FP can be interpreted as a mass-dependent evolution. Similar results have been found for cluster early-type galaxies in high redshift galaxy clusters at 0.8<z<1. Therefore, the slope change of the FP appears to be independent of the environment of the galaxies.Comment: 2 pages, 1 figure, to appear in the proceedings of the IAU Symposium no. 262, "Stellar Populations - Planning for the Next Decade", eds. G. R. Bruzual and S. Charlo