160 research outputs found
Différents points de vue pour le problème de Gribov dans les théories euclidiennes de Yang-Mills
No full textLe régime infrarouge des théories de Yang-Mills est toujours un problème insoluble en physique théorique. La tentative de décrire de manière claire et appropriée le phénomène de confinement des gluons et des quarks est loin d'être terminée. Dans ce manuscrit, nous étudions deux points de vue différents pour la quantification des théories de Yang-Mills en prenant en compte les effets des copies de Gribov. Le premier est le cadre bien connu de Gribov-Zwanziger réinventé en incluant des champs composites locaux invariants de jauge bosoniques et fermioniques grâce à une construction détaillée d'une symétrie BRST non perturbative. Cela nous donne la possibilité d'étendre ce modèle à une autre classe de jauges de manière correcte, les jauges dites covariantes linéaires. Ensuite, nous prouvons sa renormalisation à tous les ordres dans une extension de boucle en utilisant la méthode de renormalisation algébrique. L'autre est l'approche Serreau-Tissier, dans ce cadre, nous établissons une bonne explication de la génération de la masse du champ de jauge (gluon) ajoutée dans le modèle phénoménologique Curci-Ferrari particulier proposé par M. Tissier et N. Wschebor en utilisant le phénomène de restauration de symétrie. Pour ce faire, nous discutons également des similitudes entre les modèles sigma non linéaires dans deux dimensions spatio-temporelles et la chromodynamique quantique.The infrared regime of Yang-Mills theories is still an unsolvable problem in theoretical physics. The attempt to describe in a clear and suitable way the phenomenon of confinement of gluons and quarks is far from being finished. In this manuscript, we study two different viewpoints for the quantization of Yang-Mills theories by taking into account the effects of Gribov copies. The first one is the well-known Gribov-Zwanziger framework reinvented by including bosonic and fermionic gauge-invariant local composite fields through a detailed construction of a nonperturbative BRST symmetry. This gives us the possibility to extend this model to another class of gauges in a correct manner, the so-called linear covariant gauges. Then, we prove its renormalizability to all orders in a loop expansion by using the algebraic renormalization method. The other one is the Serreau-Tissier approach, in this framework we establish a good explanation for the generation of the gauge field (gluon) mass added in the particular Curci-Ferrari phenomenological model proposed by M. Tissier and N. Wschebor by using the symmetry restoration phenomenon. To accomplish that, we also discuss the similarities between the nonlinear sigma models in two space-time dimensions and quantum chromodynamics
Comment on "A structural test for the conformal invariance of the critical 3d Ising model" by S. Meneses, S. Rychkov, J. M. Viana Parente Lopes and P. Yvernay. arXiv:1802.02319
No full textIn a recent preprint [ArXiv 1802.02319], Meneses et al. challenge our proof that scale invariance implies conformal invariance for the three-dimensional Ising model [B. Delamotte, M. Tissier and N. Wschebor, Phys. Rev. E 93 (2016), 012144.]. We refute their arguments. We also point out a mistake in their one-loop calculation of the dimension of the vector operator of lowest dimension which is not a total derivative
Gribov copies, avalanches and dynamic generation of a gluon mass
No full textAnalytic calculations in the infrared regime of nonabelian gauge theories are hampered by the presence of Gribov copies which results in some ambiguity in the gauge-fixing procedure. This problem shares strong similarities with the issue of finding the true ground state among a large number of metastable states, a typical situation in the field of statistical physics of disordered systems. Building on this analogy, we propose a new gauge-fixing procedure which, we argue, makes more explicit the influence of the Gribov copies. A 1-loop calculation shows that the dynamics of these copies can lead to the spontaneous generation of a gauge-dependent gluon mass
Influence of random fields and long-range interactions on the critical behavior of the Ising model : an approach by the non pertubrative renormalization group
No full textNous étudions l’influence du champ magnétique aléatoire et des interactions à longue portée sur le comportement critique du modèle d’Ising ; notre approche est basée sur une version non perturbative et fonctionnelle du groupe de renormalisation. Les concepts du groupe de renormalisation non perturbatif sont tout d’abord introduits, puis illustrés dans le cadre simple d’une théorie classique d’un champ scalaire. Nous discutons ensuite les propriétés critiques de cette dernière en présence d’un champ magnétique aléatoire gelé qui traduit le désordre dans le système. Celui-ci est distribué comme un bruit blanc gaussien dans l’espace. Nous insistons principalement sur la propriété de réduction dimensionnelle qui prédit un comportement critique identique pour le modèle en champ aléatoire à d dimensions et le modèle pur (c’est à dire sans champ aléatoire) en dimension d − 2. Bien que cette propriété soit démontrée à tous les ordres par la théorie de perturbation, on montre que celle-ci est brisée en dessous d’une dimension critique dDR = 5.13. La réduction dimensionnelle et sa brisure sont alors reliées aux caractéristiques d’échelle des grandes avalanches intervenant dans le système à température nulle. Nous considérons, dans un second temps, une généralisation du modèle d’Ising dans laquelle l’interaction ferromagnétique décroit désormais à longue portée comme r^−(d+σ) avec σ > 0 (d désigne toujours la dimension de l’espace). Dans un tel système, il est possible de travailler en dimension fixée (incluant la dimension d = 1) et de varier l’exposant σ afin de parcourir une gamme de comportements critiques similaire à celle obtenue entre les dimensions critiques inférieure et supérieure de la version à courte portée du modèle. Nous avons caractérisé la transition de phase dans le plan (σ, d), et notamment calculé les exposants critiques en fonction du paramètre σ pour les dimensions physiquement intéressantes d = 1, 2 et 3. Finalement, on s’intéresse aussi à la théorie en présence d’un champ magnétique aléatoire dont les corrélations décroissent à grande distance comme r^−d+ρ avec ρ > −d. Dans le cas particulier où ρ = 2 − σ, on montre que la propriété de réduction dimensionnelle est vérifiée lorsque σ est suffisamment petit, mais brisée à grand σ (en dimension inférieure à σDR ). En particulier, concernant le modèle tridimensionnel, nos résultats prédisent une brisure de réduction dimensionnelle lorsque σ > σDR = 0.71.We study the influence of the presence of a random magnetic field and of long-ranged interactions on the critical behaviour of the Ising model. Our approach is based on a nonperturbative and functional version of the renormalization group. The bases of the nonperturbative renormalization group are introduced first and then illustrated in the simple case of the classical scalar field theory. We next discuss the critical properties of the latter in the presence of a random magnetic field, which is associated with frozen disorder in the system. The distribution of the random field in space is taken as that of a Gaussian white noise. We focus on the property of dimensional reduction that predicts identical critical behaviour for the random-field model in dimension d and the pure model, i.e. in the absence of random field, in dimension d-2. Although this property is found at all orders of the perturbation theory, it is violated below a critical dimension dDR = approx 5.13. We show that the dimensional reduction and its breakdown are related to the large-scale properties of the avalanches that are present in the system at zero temperature. We next consider a generalization of the Ising model in which the ferromagnetic interaction varies at large distance like r^−(d+σ) avec σ > 0 (d being the spatial dimension). In this system, it is possible to obtain a range of critical behaviour similar to that encountered in the short-ranged version of the model between the lower and the upper critical dimensions by varying the exponent σ while keeping the dimension d fixed (including the case d=1).We have characterized the phase transition of this long-ranged model in the plane (σ, d) and computed the critical exponents as a function of the parameter σ for the physically interesting dimensions, d=1, 2 and 3. Finally, we have also studied the long-ranged random-field Ising model when the correlations of the random magnetic field decrease at large distance as r^−d+ρ with ρ > −d. In the special case where ρ = 2 − σ, we have shown that the dimensional-reduction property is satisfied when σ is small enough but breaks down above a critical value (when the spatial dimension d is less than dDR). In particular, for d=3, we predict a breakdown of dimensional reduction for σ > σDR = 0.71
3. L’énergie : aspects thermodynamiques
No full textIrréversibilité et thermodynamique Un œuf roule sur une table, tombe par terre et se casse. Ceci est fâcheux, mais parfaitement acceptable physiquement. En revanche, on n’a jamais vu un œuf cassé, se reconstituer et sauter sur la table au-dessus de lui. Ces processus, qui ne se déroulent que dans un sens du temps, sont appelés irréversibles. En physique, la notion d’irréversibilité est directement reliée au second principe de la thermo-dynamique, qui nous enseigne que les différentes formes d..
Une approche non perturbative de systèmes frustrés et de systèmes désordonnés
No full textThe main part of this work consists in the study of spins submitted to competing interactions, and which are therefore frustrated. We give a detailed description of the experimental and numerical situation. We emphasize on the fact that it is necessary to go beyond perturbation theory for understanding the physical behavior of these systems. \\\indent A non-perturbative approach is therefore needed. We describe such an approach, based on an exact renormalization group equation. We discuss in details the case of vectorial models in order to show how this approach is implemented in practice, and to stress on its outstanding features. While studying frustrated systems, this non-perturbative approach indicates that these systems exhibit a weakly first order phase transition, in good agreement with experimental and numerical results. We present in the last chapter a study of the Ising model in presence of non-magnetic impurities by using the same non-perturbative approach.La majeure partie de ce travail consiste en l'étude de systèmes de spins soumis à des interactions compétitives et présentant de la frustration. Nous donnons une description détaillée de la situation expérimentale et numérique dans le domaine. Un des points cruciaux qui découle de cette analyse est la nécessité d'aller au delà des théories de perturbation pour comprendre la physique de ces systèmes. Ceci justifie d'utiliser une approche non-perturbative. Nous présentons une telle approche, basée sur une équation exacte du groupe de renormalisation. Nous discutons en détail les résultats obtenus lors de l'étude du modèle vectoriel, afin d'illustrer son utilisation dans les situations concrètes et de montrer la puissance de cette méthode. Lors de l'étude des systèmes frustrés, l'utilisation de cette méthode non-perturbative mène à la conclusion que ces systèmes présentent une transition faiblement du premier ordre. Ce comportement est en bon accord avec les résultats expérimentaux et numériques. Nous présentons dans le dernier chapitre une étude du modèle d'Ising en présence d'impuretés non magnétiques, en utilisant la même approche non perturbative
Long waves in the North Sea: Distribution, generation and measurement methods
No full textThis report presents the results of a research concerning long waves in the North Sea. ‘Long waves’ in this research is a collective name for various types of waves that are longer than the well-known sea-swell waves, here referred to as ‘short waves’. Wave types that are referred to as long waves are infragravity waves, meteo-tsunami’s, seiches and tides. Besides their extensive length, they distinguish themselves from regular sea-swell waves by the mechanisms responsible for their generation and the scale of their impact. Whereas short waves are generated by wind, long waves are generated by short wave-group forcing, the breaking of short waves nearshore and large atmospheric pressure variations. Long waves play a crucial role in the processes of coastline erosion and the breaching of flood defenses, as well as in the formation of rip currents and seiches. These events can lead to severe damage to hydraulic structures and possibly even casualties. A better understanding of them is thus vital for coastal safety.Rijkswaterstaat has been collecting data regarding the occurrence of long waves on the North Sea for over a decade. Their measurement campaign started in a time when digital broadcasting signals and digital storage space were not well developed yet, making sending and storing the water surface elevation time-series not feasible. The data is therefore filtered by a FIR filter, reducing the size of the data, but also reducing the information that is contained in the data. All frequencies of approximately 0,0125 퐻푧 and higher are removed by the FIR filter. As a consequence a significant part of the infragravity signal is missing and it is not possible to perform a bispectral analysis (used to determine the bound long wave contribution). Nowadays, digital broadcasting signals and digital storage space have plenty of capacity to send and store the data, making the filter unnecessary.Analysis of the spatial- and temporal distribution of long waves in the North Sea, shows that the majority of long waves have a yearly averaged significant wave height of 2,4 - 3,3 cm and a yearly averaged mean wave period of 125 to 140 cm. Based on data from the full decade, a clear trend in the spatial distribution of long waves cannot be distinguished, offshore and nearshore locations show approximately the same long wave properties. The seasonal analysis shows that the mean significant long wave height averaged out over all locations per season varies from 2,8 cm during summer, 2,9 cm during spring, 3,3 cm during winter to 3,5 cm during fall. For the mean wave period, the mean value averaged out over all locations per season varies from 127,5 s during summer, 128,1 s during spring, 135,6 s during winter to 136,3 s during fall. Predictions of the extreme wave conditions show that the significant wave height with a return period of 10.000 years (Dutch design condition for coastal flood defenses) are around 40-60 cm, although there is quite some uncertainty in these predictions. This uncertainty is due to a relatively short measurement period, usually 30 years of data is used for extreme wave predictions, and remarkable observations in the data.Time-series analysis of the hourly significant wave height of long waves and predicted bound long waves (Hasselmann, 1962) (Hasselmann, 1963) shows that during mild weather conditions significant wave heights of long waves are low, with minimal contributions by the bound long waves. At the onset of a storm, the significant wave height of both long waves and bound long waves rapidly increase. At the end of the storm, they decrease to the pre-storm values. This shows that the generation of long waves occurs mainly during heavy weather conditions. Hourly significant wave heights of long waves, and especially bound long waves, show a strong correlation with significant short wave heights. The relative contribution of bound long waves (퐸푏푙푤/퐸푙푤) during a storm increases up to values of 60%, which is considerably higher than contributions of bound long waves found in other studies (Herbers et al., 1994). The high ratio of the relative bound long wave contribution, in combination with very low bound long wave activity during mild conditions, shows that the generation mechanism involving wave-group forcing is a major generation mechanism of long waves in the North Sea
Random-field Ising and
No full textWe review the theoretical description of the random field Ising and O(N) models obtained from the functional renormalization group, either in its nonperturbative implementation or, in some limits, in perturbative implementations. The approach solves questions concerning the critical behavior of random-field systems that have stayed pending for many years: What is the mechanism for the breakdown of dimensional reduction and the breaking of the underlying supersymmetry below d = 6? Can one provide a theoretical computation of the critical exponents, including the exponent ψ characterizing the activated dynamic scaling? Is it possible to theoretically describe collective phenomena such as avalanches and droplets? Is the critical scaling described by 2 or 3 independent exponents? What is the phase behavior of the random-field O(N) model in the whole (N, d) plane and what is the lower critical dimension of quasi-long range order for N = 2? Are the equilibrium and out-of-equilibrium critical points of the RFIM in the same universality class
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