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

Regenerative approaches for V/UHTS feeder links: system analysis and on-board complexity reduction

The dramatically increasing demand for high data rates necessitates the proper dimensioning of the feeder links of very or ultra high throughput satellite (V/UHTS) systems. However, because most of the current solutions rely on transparent payloads, the deployment of a very large number of spatially separated ground stations is necessary to support the total system bandwidth by enabling a full reuse of the scarce available uplink bandwidth. This approach has a significant impact on the complexity and the costs of the ground segment infrastructure. Regenerative payloads could be considered to avoid this design bottleneck. By allowing demodulation and decoding on-board the satellite, the favourable link budget conditions of feeder links compared to the user links can be exploited. Using a spectral efficient transmission technique, the number of ground stations required to support a target sum throughput can be notably reduced. Meanwhile, regenerative solutions have until now barely been used in V/UHTS payloads due to their high on-board power consumption. As a consequence, candidate solutions are proposed in this work to overcome this limitation. A non-coherent modulation technique, known as Differential Amplitude Phase Shift Keying (DAPSK), is introduced to avoid on-board carrier synchronization. Moreover, polar codes are considered to minimize the power consumption of the channel decoder. A preliminary analysis of the expected on-board power consumption compared to that of a standard DVB-S2 approach is conducted using available results in the open literature. Link performance is also evaluated via numerical simulations

Functional renormalization group in the broken symmetry phase: momentum dependence and two-parameter scaling of the self-energy

We include spontaneous symmetry breaking into the functional renormalization group (RG) equations for the irreducible vertices of Ginzburg-Landau theories by augmenting these equations by a flow equation for the order parameter, which is determined from the requirement that at each RG step the vertex with one external leg vanishes identically. Using this strategy, we propose a simple truncation of the coupled RG flow equations for the vertices in the broken symmetry phase of the Ising universality class in D dimensions. Our truncation yields the full momentum dependence of the self-energy Sigma (k) and interpolates between lowest order perturbation theory at large momenta k and the critical scaling regime for small k. Close to the critical point, our method yields the self-energy in the scaling form Sigma (k) = k_c^2 sigma^{-} (k | xi, k / k_c), where xi is the order parameter correlation length, k_c is the Ginzburg scale, and sigma^{-} (x, y) is a dimensionless two-parameter scaling function for the broken symmetry phase which we explicitly calculate within our truncation.Comment: 9 pages, 4 figures, puplished versio

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

Non-perturbative renormalization-group approach to zero-temperature Bose systems

We use a non-perturbative renormalization-group technique to study interacting bosons at zero temperature. Our approach reveals the instability of the Bogoliubov fixed point when $d\leq 3$ and yields the exact infrared behavior in all dimensions $d>1$ within a rather simple theoretical framework. It also enables to compute the low-energy properties in terms of the parameters of a microscopic model. In one-dimension and for not too strong interactions, it yields a good picture of the Luttinger-liquid behavior of the superfluid phase.Comment: v1) 6 pages, 8 figures; v2) added references; v3) corrected typo

Equivalent Fixed-Points in the Effective Average Action Formalism

Starting from a modified version of Polchinski's equation, Morris' fixed-point equation for the effective average action is derived. Since an expression for the line of equivalent fixed-points associated with every critical fixed-point is known in the former case, this link allows us to find, for the first time, the analogous expression in the latter case.Comment: 30 pages; v2: 29 pages - major improvements to section 3; v3: published in J. Phys. A - minor change

Heisenberg frustrated magnets: a nonperturbative approach

Frustrated magnets are a notorious example where the usual perturbative methods are in conflict. Using a nonperturbative Wilson-like approach, we get a coherent picture of the physics of Heisenberg frustrated magnets everywhere between $d=2$ and $d=4$. We recover all known perturbative results in a single framework and find the transition to be weakly first order in $d=3$. We compute effective exponents in good agreement with numerical and experimental data.Comment: 5 pages, Revtex, technical details available at http://www.lpthe.jussieu.fr/~tissie

Critical behavior of frustrated systems: Monte Carlo simulations versus Renormalization Group

We study the critical behavior of frustrated systems by means of Pade-Borel resummed three-loop renormalization-group expansions and numerical Monte Carlo simulations. Amazingly, for six-component spins where the transition is second order, both approaches disagree. This unusual situation is analyzed both from the point of view of the convergence of the resummed series and from the possible relevance of non perturbative effects.Comment: RevTex, 10 pages, 3 Postscript figure

A non perturbative approach of the principal chiral model between two and four dimensions

We investigate the principal chiral model between two and four dimensions by means of a non perturbative Wilson-like renormalization group equation. We are thus able to follow the evolution of the effective coupling constants within this whole range of dimensions without having recourse to any kind of small parameter expansion. This allows us to identify its three dimensional critical physics and to solve the long-standing discrepancy between the different perturbative approaches that characterizes the class of models to which the principal chiral model belongs.Comment: 5 pages, 1 figure, Revte