Susceptibility Amplitude Ratios Near a Lifshitz Point

The susceptibility amplitude ratio in the neighborhood of a uniaxial Lifshitz point is calculated at one-loop level using field-theoretic and $\epsilon_{L}$-expansion methods. We use the Schwinger parametrization of the propagator in order to split the quadratic and quartic part of the momenta, as well as a new special symmetry point suitable for renormalization purposes. For a cubic lattice (d = 3), we find the result $\frac{C_{+}}{C_{-}} = 3.85$.Comment: 7 pages, late

On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three

In the present paper we study forward Quantum Markov Chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY-model on a Cayley tree of order three in QMC scheme. By the phase transition we mean the existence of two now quasi equivalent QMC for the given family of interaction operators $\{K_{}\}$.Comment: 34 pages, 1 figur

Boundary critical behavior at m-axial Lifshitz points for a boundary plane parallel to the modulation axes

The critical behavior of semi-infinite $d$-dimensional systems with $n$-component order parameter $\bm{\phi}$ and short-range interactions is investigated at an $m$-axial bulk Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional subspace of $\mathbb{R}^d$. The associated $m$ modulation axes are presumed to be parallel to the surface, where $0\le m\le d-1$. An appropriate semi-infinite $|\bm{\phi}|^4$ model representing the corresponding universality classes of surface critical behavior is introduced. It is shown that the usual O(n) symmetric boundary term $\propto \bm{\phi}^2$ of the Hamiltonian must be supplemented by one of the form $\mathring{\lambda} \sum_{\alpha=1}^m(\partial\bm{\phi}/\partial x_\alpha)^2$ involving a dimensionless (renormalized) coupling constant $\lambda$. The implied boundary conditions are given, and the general form of the field-theoretic renormalization of the model below the upper critical dimension $d^*(m)=4+{m}/{2}$ is clarified. Fixed points describing the ordinary, special, and extraordinary transitions are identified and shown to be located at a nontrivial value $\lambda^*$ if $\epsilon\equiv d^*(m)-d>0$. The surface critical exponents of the ordinary transition are determined to second order in $\epsilon$. Extrapolations of these $\epsilon$ expansions yield values of these exponents for $d=3$ in good agreement with recent Monte Carlo results for the case of a uniaxial ($m=1$) Lifshitz point. The scaling dimension of the surface energy density is shown to be given exactly by $d+m (\theta-1)$, where $\theta=\nu_{l4}/\nu_{l2}$ is the anisotropy exponent.Comment: revtex4, 31 pages with eps-files for figures, uses texdraw to generate some graphs; to appear in PRB; v2: some references and additional remarks added, labeling in figure 1 and some typos correcte

Susceptibility amplitude ratio for generic competing systems

We calculate the susceptibility amplitude ratio near a generic higher character Lifshitz point up to one-loop order. We employ a renormalization group treatment with $L$ independent scaling transformations associated to the various inequivalent subspaces in the anisotropic case in order to compute the ratio above and below the critical temperature and demonstrate its universality. Furthermore, the isotropic results with only one type of competition axes have also been shown to be universal. We describe how the simpler situations of $m$-axial Lifshitz points as well as ordinary (noncompeting) systems can be retrieved from the present framework.Comment: 20 pages, no figure

Persistent Spin Currents in Helimagnets

We demonstrate that weak external magnetic fields generate dissipationless spin currents in the ground state of systems with spiral magnetic order. Our conclusions are based on phenomenological considerations and on microscopic mean-field theory calculations for an illustrative toy model. We speculate on possible applications of this effect in spintronic devices.Comment: 9 pages, 6 figures, updated version as published, Journal referenc

Authenticity and Racism: Young boys in three inner city primary schools in Dublin

This paper examines the role of authenticity as a moral orientation and social evaluation in practices of racism. It will argue that discursive conceptions of authenticity disguise and legitimise racism within micro encounters. Using evidence from a qualitative study of minority children in Ireland, this paper explores how perceptions of ‘authenticity’ are bound within racist and gendered conceptions of whom can be said to legitimately embody nationally and locally authorised dispositions and identity markers. The specific context of how this played out through the locality of north Dublin and constructed notions of Irishness is examined. The wider implications of a discourse of authenticity are discussed in relation to assumptions of similarity, adaptation and integration. This paper contributes two unique insights, firstly, that the passive body (one’s appearance) has a central role in perceptions of authenticity and, secondly, that similarity in one’s active body (dispositions and tastes) does not necessarily act as a bridge to bring racialised groups together or facilitate integration