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

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

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

Two-loop Functional Renormalization Group of the Random Field and Random Anisotropy O(N) Models

We study by the perturbative Functional Renormalization Group (FRG) the Random Field and Random Anisotropy O(N) models near $d=4$, the lower critical dimension of ferromagnetism. The long-distance physics is controlled by zero-temperature fixed points at which the renormalized effective action is nonanalytic. We obtain the beta functions at 2-loop order, showing that despite the nonanalytic character of the renormalized effective action, the theory is perturbatively renormalizable at this order. The physical results obtained at 2-loop level, most notably concerning the breakdown of dimensional reduction at the critical point and the stability of quasi-long range order in $d<4$, are shown to fit into the picture predicted by our recent non-perturbative FRG approach.Comment: 19 pages, 20 figures. Minor correction

Auxiliary fields approach to shift-symmetric theories: the φ4\varphi^4 derivative theory and the crumpled-to-flat transition of membranes at two-loop order

We introduce a technique relying on the use of auxiliary fields in order to eliminate explicit field-derivatives that plague the high orders renormalization group treatment of shift-symmetric, derivative, theories. This technique simplifies drastically the computation of fluctuations in such theories. This is illustrated by deriving the two-loop renormalization group equations and the three-loop anomalous dimension of the $\varphi^4$ derivative theory in $D=4-\epsilon$, which is also relevant to describe the crumpled-to-flat transition of polymerized membranes. Some features of this transition are provided.Comment: 7 page

An Infrared Safe perturbative approach to Yang-Mills correlators

We investigate the 2-point correlation functions of Yang-Mills theory in the Landau gauge by means of a massive extension of the Faddeev-Popov action. This model is based on some phenomenological arguments and constraints on the ultraviolet behavior of the theory. We show that the running coupling constant remains finite at all energy scales (no Landau pole) for $d>2$ and argue that the relevant parameter of perturbation theory is significantly smaller than 1 at all energies. Perturbative results at low orders are therefore expected to be satisfactory and we indeed find a very good agreement between 1-loop correlation functions and the lattice simulations, in 3 and 4 dimensions. Dimension 2 is shown to play the role of an upper critical dimension, which explains why the lattice predictions are qualitatively different from those in higher dimensions.Comment: 16 pages, 7 figures, accepted for publication in PR

Методические особенности управления туристскими потоками в регионе (на примере Автономной Республики Крым)

Экономическая жизнь, начиная от простых жителей сел и городов, до экономики полуострова в целом зависит от количества туристов, приехавших в Крым на отдых и лечениеЕкономічне життя, починаючи від простих мешканців сіл і міст, до економіки півострова в цілому залежить від кількості туристів, що приїхали до Криму на відпочинок і лікуванн

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