Ferromagnetism in defect-ridden oxides and related materials

The existence of high-temperature ferromagnetism in thin films and nanoparticles of oxides containing small quantities of magnetic dopants remains controversial. Some regard these materials as dilute magnetic semiconductors, while others think they are ferromagnetic only because the magnetic dopants form secondary ferromagnetic impurity phases such as cobalt metal or magnetite. There are also reports in d0 systems and other defective oxides that contain no magnetic ions. Here, we investigate TiO2 (rutile) containing 1 - 5% of iron cations and find that the room-temperature ferromagnetism of films prepared by pulsed-laser deposition is not due to magnetic ordering of the iron. The films are neither dilute magnetic semiconductors nor hosts to an iron-based ferromagnetic impurity phase. A new model is developed for defect-related ferromagnetism which involves a spin-split defect band populated by charge transfer from a proximate charge reservoir in the present case a mixture Fe2+ and Fe3+ ions in the oxide lattice. The phase diagram for the model shows how inhomogeneous Stoner ferromagnetism depends on the total number of electrons Ntot, the Stoner exchange integral I and the defect bandwidth W; the band occupancy is governed by the d-d Coulomb interaction U. There are regions of ferromagnetic metal, half-metal and insulator as well as nonmagnetic metal and insulator. A characteristic feature of the high-temperature Stoner magnetism is an an anhysteretic magnetization curve which is practically temperature independent below room temperature. This is related to a wandering ferromagnetic axis which is determined by local dipole fields. The magnetization is limited by the defect concentration, not by the 3d doping. Only 1-2 % of the volume of the films is magnetically ordered.Comment: 22 pages, 6 figure

The Complex Langevin method: When can it be trusted?

We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.Comment: 14 pages, including several eps figures and tables; clarification and minor corrections added, to appear in PR

From the 'cinematic' to the 'anime-ic': Issues of movement in anime

This is the author's accepted manuscript. The final published article is available from the link below.This article explores the way that movement is formally depicted in anime. Drawing on Thomas Lamarre's concepts of the `cinematic' and the `anime-ic', the article interrogates further the differences in movement and action in anime from traditional filmic form. While often considered in terms of `flatness', anime offers spectacle, character development and, ironically, depth through the very form of movement put to use in such texts.The article questions whether the modes of address at work in anime are unique to this form of animation.Taking into account how the terms `cinematic' and `anime-ic' can be understood (and by extension the cinematic and animatic apparatus), the article also begins to explore how viewers might identify with such images

Integral equations PS-3 and moduli of pants

More than a hundred years ago H.Poincare and V.A.Steklov considered a problem for the Laplace equation with spectral parameter in the boundary conditions. Today similar problems for two adjacent domains with the spectral parameter in the conditions on the common boundary of the domains arises in a variety of situations: in justification and optimization of domain decomposition method, simple 2D models of oil extraction, (thermo)conductivity of composite materials. Singular 1D integral Poincare-Steklov equation with spectral parameter naturally emerges after reducing this 2D problem to the common boundary of the domains. We present a constructive representation for the eigenvalues and eigenfunctions of this integral equation in terms of moduli of explicitly constructed pants, one of the simplest Riemann surfaces with boundary. Essentially the solution of integral equation is reduced to the solution of three transcendent equations with three unknown numbers, moduli of pants. The discreet spectrum of the equation is related to certain surgery procedure ('grafting') invented by B.Maskit (1969), D.Hejhal (1975) and D.Sullivan- W.Thurston (1983).Comment: 27 pages, 13 figure

Menelaus relation and Fay's trisecant formula are associativity equations

It is shown that the celebrated Menelaus relation and Fay's trisecant formula similar to the WDVV equation are associativity conditions for structure constants of certain three-dimensional algebra.Comment: Talk given at the Conference " Mathematics and Physics of Solitons and Integrable Systems", Dijon, 28.6-2.7, 2009. Minor misprints correcte

Two dimensional Sen connections and quasi-local energy-momentum

The recently constructed two dimensional Sen connection is applied in the problem of quasi-local energy-momentum in general relativity. First it is shown that, because of one of the two 2 dimensional Sen--Witten identities, Penrose's quasi-local charge integral can be expressed as a Nester--Witten integral.Then, to find the appropriate spinor propagation laws to the Nester--Witten integral, all the possible first order linear differential operators that can be constructed only from the irreducible chiral parts of the Sen operator alone are determined and examined. It is only the holomorphy or anti-holomorphy operator that can define acceptable propagation laws. The 2 dimensional Sen connection thus naturally defines a quasi-local energy-momentum, which is precisely that of Dougan and Mason. Then provided the dominant energy condition holds and the 2-sphere S is convex we show that the next statements are equivalent: i. the quasi-local mass (energy-momentum) associated with S is zero; ii.the Cauchy development $D(\Sigma)$ is a pp-wave geometry with pure radiation ($D(\Sigma)$ is flat), where $\Sigma$ is a spacelike hypersurface whose boundary is S; iii. there exist a Sen--constant spinor field (two spinor fields) on S. Thus the pp-wave Cauchy developments can be characterized by the geometry of a two rather than a three dimensional submanifold.Comment: 20 pages, Plain Tex, I

New fields on super Riemann surfaces

A new $(1,1)$-dimensional super vector bundle which exists on any super Riemann surface is described. Cross-sections of this bundle provide a new class of fields on a super Riemann surface which closely resemble holomorphic functions on a super Riemann surface, but which (in contrast to the case with holomorphic functions) form spaces which have a well defined dimension which does not change as odd moduli become non-zero.Comment: 12pp, kcl-th-94-

Entire curves avoiding given sets in C^n

Let $F\subset\Bbb C^n$ be a proper closed subset of $\Bbb C^n$ and $A\subset\Bbb C^n\setminus F$ at most countable ($n\geq 2$). We give conditions of $F$ and $A$, under which there exists a holomorphic immersion (or a proper holomorphic embedding) $\phi:\Bbb C\to\Bbb C^n$ with $A\subset\phi(\Bbb C)\subset\Bbb C^n\setminus F$.Comment: 10 page

New Jacobi-Like Identities for Z_k Parafermion Characters

We state and prove various new identities involving the Z_K parafermion characters (or level-K string functions) for the cases K=4, K=8, and K=16. These identities fall into three classes: identities in the first class are generalizations of the famous Jacobi theta-function identity (which is the K=2 special case), identities in another class relate the level K>2 characters to the Dedekind eta-function, and identities in a third class relate the K>2 characters to the Jacobi theta-functions. These identities play a crucial role in the interpretation of fractional superstring spectra by indicating spacetime supersymmetry and aiding in the identification of the spacetime spin and statistics of fractional superstring states.Comment: 72 pages (or 78/2 = 39 pages in reduced format

On Holomorphic Factorization in Asymptotically AdS 3D Gravity

This paper studies aspects of ``holography'' for Euclidean signature pure gravity on asymptotically AdS 3-manifolds. This theory can be described as SL(2,C) CS theory. However, not all configurations of CS theory correspond to asymptotically AdS 3-manifolds. We show that configurations that do have the metric interpretation are parameterized by the so-called projective structures on the boundary. The corresponding asymptotic phase space is shown to be the cotangent bundle over the Schottky space of the boundary. This singles out a ``gravitational'' sector of the SL(2,C) CS theory. It is over this sector that the path integral has to be taken to obtain the gravity partition function. We sketch an argument for holomorphic factorization of this partition function.Comment: 32+1 pages, no figures; (v2) one reference added, a statement regarding priorities modified; (v3) presentational changes, an important sign mistake correcte