498 research outputs found
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 , 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 , 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 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 derivative
theory in , 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 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
ΠΠ΅ΡΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠΈ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΡΡΡΠΈΡΡΡΠΊΠΈΠΌΠΈ ΠΏΠΎΡΠΎΠΊΠ°ΠΌΠΈ Π² ΡΠ΅Π³ΠΈΠΎΠ½Π΅ (Π½Π° ΠΏΡΠΈΠΌΠ΅ΡΠ΅ ΠΠ²ΡΠΎΠ½ΠΎΠΌΠ½ΠΎΠΉ Π Π΅ΡΠΏΡΠ±Π»ΠΈΠΊΠΈ ΠΡΡΠΌ)
ΠΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΆΠΈΠ·Π½Ρ, Π½Π°ΡΠΈΠ½Π°Ρ ΠΎΡ ΠΏΡΠΎΡΡΡΡ
ΠΆΠΈΡΠ΅Π»Π΅ΠΉ ΡΠ΅Π» ΠΈ Π³ΠΎΡΠΎΠ΄ΠΎΠ², Π΄ΠΎ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΠΊΠΈ ΠΏΠΎΠ»ΡΠΎΡΡΡΠΎΠ²Π° Π² ΡΠ΅Π»ΠΎΠΌ Π·Π°Π²ΠΈΡΠΈΡ ΠΎΡ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° ΡΡΡΠΈΡΡΠΎΠ², ΠΏΡΠΈΠ΅Ρ
Π°Π²ΡΠΈΡ
Π² ΠΡΡΠΌ Π½Π° ΠΎΡΠ΄ΡΡ
ΠΈ Π»Π΅ΡΠ΅Π½ΠΈΠ΅ΠΠΊΠΎΠ½ΠΎΠΌΡΡΠ½Π΅ ΠΆΠΈΡΡΡ, ΠΏΠΎΡΠΈΠ½Π°ΡΡΠΈ Π²ΡΠ΄ ΠΏΡΠΎΡΡΠΈΡ
ΠΌΠ΅ΡΠΊΠ°Π½ΡΡΠ² ΡΡΠ» Ρ ΠΌΡΡΡ, Π΄ΠΎ Π΅ΠΊΠΎΠ½ΠΎΠΌΡΠΊΠΈ ΠΏΡΠ²ΠΎΡΡΡΠΎΠ²Π° Π² ΡΡΠ»ΠΎΠΌΡ Π·Π°Π»Π΅ΠΆΠΈΡΡ Π²ΡΠ΄ ΠΊΡΠ»ΡΠΊΠΎΡΡΡ ΡΡΡΠΈΡΡΡΠ², ΡΠΎ ΠΏΡΠΈΡΡ
Π°Π»ΠΈ Π΄ΠΎ ΠΡΠΈΠΌΡ Π½Π° Π²ΡΠ΄ΠΏΠΎΡΠΈΠ½ΠΎΠΊ Ρ Π»ΡΠΊΡΠ²Π°Π½Π½
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
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