An exact renormalization group approach to frustrated magnets

Frustrated magnets are a notorious example where usual perturbative methods fail. Having recourse to an exact renormalization group approach, one gets a coherent picture of the physics of Heisenberg frustrated magnets everywhere between d=2 and d=4: all known perturbative results are recovered in a single framework, their apparent conflict is explained while the description of the phase transition in d=3 is found to be in good agreement with the experimental context.Comment: 4 pages, Latex, invited talk at the Second Conference on the Exact Renormalization Group, Rome, September 2000, for technical details see http://www.lpthe.jussieu.fr/~tissie

Critical properties of a continuous family of XY noncollinear magnets

Monte Carlo methods are used to study a family of three dimensional XY frustrated models interpolating continuously between the stacked triangular antiferromagnets and a variant of this model for which a local rigidity constraint is imposed. Our study leads us to conclude that generically weak first order behavior occurs in this family of models in agreement with a recent nonperturbative renormalization group description of frustrated magnets.Comment: 5 pages, 3 figures, minor changes, published versio

Frustrated magnets in three dimensions: a nonperturbative approach

Frustrated magnets exhibit unusual critical behaviors: they display scaling laws accompanied by nonuniversal critical exponents. This suggests that these systems generically undergo very weak first order phase transitions. Moreover, the different perturbative approaches used to investigate them are in conflict and fail to correctly reproduce their behavior. Using a nonperturbative approach we explain the mismatch between the different perturbative approaches and account for the nonuniversal scaling observed.Comment: 7 pages, 1 figure. IOP style files included. To appear in Journal of Physics: Condensed Matter. Proceedings of the conference HFM 2003, Grenoble, Franc

Characterisation of a mural cell network in the murine pituitary gland

The anterior and intermediate lobes of the pituitary are composed of endocrine cells, as well as vasculature and supporting cells, such as folliculostellate cells. Folliculostellate cells form a network with several postulated roles in the pituitary, including production of paracrine signalling molecules and cytokines, coordination of endocrine cell hormone release, phagocytosis, and structural support. Folliculostellate cells in rats are characterised by expression of S100B protein, and in humans by glial fibrillary acid protein. However, there is evidence for another network of supporting cells in the anterior pituitary that has properties of mural cells, such as vascular smooth muscle cells and pericytes. The present study aims to characterise the distribution of cells that express the mural cell marker platelet derived growth factor receptor beta (PDGFRβ) in the mouse pituitary and establish whether these cells are folliculostellate. By immunohistochemical localisation, we determine that approximately 80% of PDGFRβ+ cells in the mouse pituitary have a non‐perivascular location and 20% are pericytes. Investigation of gene expression in a magnetic cell sorted population of PDGFRβ+ cells shows that, despite a mostly non‐perivascular location, this population is enriched for mural cell markers but not enriched for rat or human folliculostellate cell markers. This is confirmed by immunohistochemistry. The present study concludes that a mural cell network is present throughout the anterior pituitary of the mouse and that this population does not express well‐characterised human or rat folliculostellate cell markers

Fixed points in frustrated magnets revisited

We analyze the validity of perturbative renormalization group estimates obtained within the fixed dimension approach of frustrated magnets. We reconsider the resummed five-loop beta-functions obtained within the minimal subtraction scheme without epsilon-expansion for both frustrated magnets and the well-controlled ferromagnetic systems with a cubic anisotropy. Analyzing the convergence properties of the critical exponents in these two cases we find that the fixed point supposed to control the second order phase transition of frustrated magnets is very likely an unphysical one. This is supported by its non-Gaussian character at the upper critical dimension d=4. Our work confirms the weak first order nature of the phase transition occuring at three dimensions and provides elements towards a unified picture of all existing theoretical approaches to frustrated magnets.Comment: 18 pages, 8 figures. This article is an extended version of arXiv:cond-mat/060928

Spin-stiffness and topological defects in two-dimensional frustrated spin systems

Using a {\it collective} Monte Carlo algorithm we study the low-temperature and long-distance properties of two systems of two-dimensional classical tops. Both systems have the same spin-wave dynamics (low-temperature behavior) as a large class of Heisenberg frustrated spin systems. They are constructed so that to differ only by their topological properties. The spin-stiffnesses for the two systems of tops are calculated for different temperatures and different sizes of the sample. This allows to investigate the role of topological defects in frustrated spin systems. Comparisons with Renormalization Group results based on a Non Linear Sigma model approach and with the predictions of some simple phenomenological model taking into account the topological excitations are done.Comment: RevTex, 25 pages, 14 figures, Minor changes, final version. To appear in Phys.Rev.

On the leading OPE corrections to the ghost-gluon vertex and the Taylor theorem

This brief note is devoted to a study of genuine non-perturbative corrections to the Landau gauge ghost-gluon vertex in terms of the non-vanishing dimension-two gluon condensate. We pay special attention to the kinematical limit which the bare vertex takes for its tree-level expression at any perturbative order, according to the well-known Taylor theorem. Based on our OPE analysis, we also present a simple model for the vertex, in acceptable agreement with lattice data.Comment: Final version published in JHE

Spin Stiffness of Stacked Triangular Antiferromagnets

We study the spin stiffness of stacked triangular antiferromagnets using both heat bath and broad histogram Monte Carlo methods. Our results are consistent with a continuous transition belonging to the chiral universality class first proposed by Kawamura.Comment: 5 pages, 7 figure