55 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
Functional renormalization group approach to non-collinear magnets
A functional renormalization group approach to -dimensional,
-component, non-collinear magnets is performed using various truncations of
the effective action relevant to study their long distance behavior. With help
of these truncations we study the existence of a stable fixed point for
dimensions between and for various values of focusing on the
critical value that, for a given dimension , separates a first
order region for . Our
approach concludes to the absence of stable fixed point in the physical -
and - cases, in agreement with -expansion and in
contradiction with previous perturbative approaches performed at fixed
dimension and with recent approaches based on conformal bootstrap program.Comment: 16 pages, 8 figure
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
Monte Carlo Calculation of the Spin-Stiffness of the Two-Dimensional Heisenberg Model
Using a collective-mode Monte Carlo method (the Wolff-Swendsen-Wang
algorithm), we compute the spin-stiffness of the two-dimensional classical
Heisenberg model. We show that it is the relevant physical quantity to
investigate the behaviour of the model in the very low temperature range
inaccessible to previous studies based on correlation length and susceptibility
calculations.Comment: 6 pages, latex, 3 postscript figures appended, DIM preprint 93-3
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
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
Spontaneous versus explicit replica symmetry breaking in the theory of disordered systems
We investigate the relation between spontaneous and explicit replica symmetry
breaking in the theory of disordered systems. On general ground, we prove the
equivalence between the replicon operator associated with the stability of the
replica symmetric solution in the standard replica scheme and the operator
signaling a breakdown of the solution with analytic field dependence in a
scheme in which replica symmetry is explicitly broken by applied sources. This
opens the possibility to study, via the recently developed functional
renormalization group, unresolved questions related to spontaneous replica
symmetry breaking and spin-glass behavior in finite-dimensional disordered
systems.Comment: 16 page
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
Analysis of the 3d massive renormalization group perturbative expansions: a delicate case
The effectiveness of the perturbative renormalization group approach at fixed space dimension d in the theory of critical phenomena is analyzed. Three models are considered: the O(N) model, the cubic model and the antiferromagnetic model defined on the stacked triangular lattice. We consider all models at fixed d = 3 and analyze the resummation procedures currently used to compute the critical exponents. We first show that, for the O(N) model, the resummation does not eliminate all non-physical (spurious) fixed points (FPs). Then the dependence of spurious as well as of the Wilson-Fisher FPs on the resummation parameters is carefully studied. The critical exponents at the Wilson-Fisher FP show a weak dependence on the resummation parameters. On the contrary, the exponents at the spurious FP as well as its very existence are strongly dependent on these parameters. For the cubic model, a new stable FP is found and its properties depend also strongly on the resummation parameters. It appears to be spurious, as expected. As for the frustrated models, there are two cases depending on the value of the number of spin components. When N is greater than a critical value Nc, the stable FP shows common characteristic with the Wilson-Fisher FP. On the contrary, for N 3, we conclude that the transitions for XY and Heisenberg frustrated magnets are of first order
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