Wilson-Polchinski exact renormalization group equation for O(N) systems: Leading and next-to-leading orders in the derivative expansion

With a view to study the convergence properties of the derivative expansion of the exact renormalization group (RG) equation, I explicitly study the leading and next-to-leading orders of this expansion applied to the Wilson-Polchinski equation in the case of the $N$-vector model with the symmetry $\mathrm{O}(N)$. As a test, the critical exponents $$ and $\nu$ as well as the subcritical exponent $\omega$ (and higher ones) are estimated in three dimensions for values of $N$ ranging from 1 to 20. I compare the results with the corresponding estimates obtained in preceding studies or treatments of other $\mathrm{O}(N)$ exact RG equations at second order. The possibility of varying $N$ allows to size up the derivative expansion method. The values obtained from the resummation of high orders of perturbative field theory are used as standards to illustrate the eventual convergence in each case. A peculiar attention is drawn on the preservation (or not) of the reparametrisation invariance.Comment: Dedicated to Lothar Sch\"afer on the occasion of his 60th birthday. Final versio

The nonperturbative functional renormalization group and its applications

The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for viable ultraviolet completions in fundamental physics. It provides us with a natural framework to study theoretical models where degrees of freedom are correlated over long distances and that may exhibit very distinct behavior on different energy scales. The nonperturbative functional renormalization-group (FRG) approach is a modern implementation of Wilson's RG, which allows one to set up nonperturbative approximation schemes that go beyond the standard perturbative RG approaches. The FRG is based on an exact functional flow equation of a coarse-grained effective action (or Gibbs free energy in the language of statistical mechanics). We review the main approximation schemes that are commonly used to solve this flow equation and discuss applications in equilibrium and out-of-equilibrium statistical physics, quantum many-particle systems, high-energy physics and quantum gravity.Comment: v2) Review article, 93 pages + bibliography, 35 figure

Towards Classification of Phase Transitions in Reaction--Diffusion Models

Equilibrium phase transitions are associated with rearrangements of minima of a (Lagrangian) potential. Treatment of non-equilibrium systems requires doubling of degrees of freedom, which may be often interpreted as a transition from the ``coordinate'' to the ``phase'' space representation. As a result, one has to deal with the Hamiltonian formulation of the field theory instead of the Lagrangian one. We suggest a classification scheme of phase transitions in reaction-diffusion models based on the topology of the phase portraits of corresponding Hamiltonians. In models with an absorbing state such a topology is fully determined by intersecting curves of zero ``energy''. We identify four families of topologically distinct classes of phase portraits stable upon RG transformations.Comment: 14 pages, 9 figure

Rationale and study design of PROVHILO - a worldwide multicenter randomized controlled trial on protective ventilation during general anesthesia for open abdominal surgery

<p>Abstract</p> <p>Background</p> <p>Post-operative pulmonary complications add to the morbidity and mortality of surgical patients, in particular after general anesthesia >2 hours for abdominal surgery. Whether a protective mechanical ventilation strategy with higher levels of positive end-expiratory pressure (PEEP) and repeated recruitment maneuvers; the "open lung strategy", protects against post-operative pulmonary complications is uncertain. The present study aims at comparing a protective mechanical ventilation strategy with a conventional mechanical ventilation strategy during general anesthesia for abdominal non-laparoscopic surgery.</p> <p>Methods</p> <p>The PROtective Ventilation using HIgh versus LOw positive end-expiratory pressure ("PROVHILO") trial is a worldwide investigator-initiated multicenter randomized controlled two-arm study. Nine hundred patients scheduled for non-laparoscopic abdominal surgery at high or intermediate risk for post-operative pulmonary complications are randomized to mechanical ventilation with the level of PEEP at 12 cmH₂O with recruitment maneuvers (the lung-protective strategy) or mechanical ventilation with the level of PEEP at maximum 2 cmH₂O without recruitment maneuvers (the conventional strategy). The primary endpoint is any post-operative pulmonary complication.</p> <p>Discussion</p> <p>The PROVHILO trial is the first randomized controlled trial powered to investigate whether an open lung mechanical ventilation strategy in short-term mechanical ventilation prevents against postoperative pulmonary complications.</p> <p>Trial registration</p> <p>ISRCTN: <a href="http://www.controlled-trials.com/ISRCTN70332574">ISRCTN70332574</a></p

Phase Structure and Compactness

In order to study the influence of compactness on low-energy properties, we compare the phase structures of the compact and non-compact two-dimensional multi-frequency sine-Gordon models. It is shown that the high-energy scaling of the compact and non-compact models coincides, but their low-energy behaviors differ. The critical frequency $\beta^2 = 8\pi$ at which the sine-Gordon model undergoes a topological phase transition is found to be unaffected by the compactness of the field since it is determined by high-energy scaling laws. However, the compact two-frequency sine-Gordon model has first and second order phase transitions determined by the low-energy scaling: we show that these are absent in the non-compact model.Comment: 21 pages, 5 figures, minor changes, final version, accepted for publication in JHE

Introduction to the functional RG and applications to gauge theories

These lectures contain an introduction to modern renormalization group (RG) methods as well as functional RG approaches to gauge theories. In the first lecture, the functional renormalization group is introduced with a focus on the flow equation for the effective average action. The second lecture is devoted to a discussion of flow equations and symmetries in general, and flow equations and gauge symmetries in particular. The third lecture deals with the flow equation in the background formalism which is particularly convenient for analytical computations of truncated flows. The fourth lecture concentrates on the transition from microscopic to macroscopic degrees of freedom; even though this is discussed here in the language and the context of QCD, the developed formalism is much more general and will be useful also for other systems.Comment: 60 pages, 14 figures, Lectures held at the 2006 ECT* School "Renormalization Group and Effective Field Theory Approaches to Many-Body Systems", Trento, Ital

Nonperturbative renormalization group approach to frustrated magnets

This article is devoted to the study of the critical properties of classical XY and Heisenberg frustrated magnets in three dimensions. We first analyze the experimental and numerical situations. We show that the unusual behaviors encountered in these systems, typically nonuniversal scaling, are hardly compatible with the hypothesis of a second order phase transition. We then review the various perturbative and early nonperturbative approaches used to investigate these systems. We argue that none of them provides a completely satisfactory description of the three-dimensional critical behavior. We then recall the principles of the nonperturbative approach - the effective average action method - that we have used to investigate the physics of frustrated magnets. First, we recall the treatment of the unfrustrated - O(N) - case with this method. This allows to introduce its technical aspects. Then, we show how this method unables to clarify most of the problems encountered in the previous theoretical descriptions of frustrated magnets. Firstly, we get an explanation of the long-standing mismatch between different perturbative approaches which consists in a nonperturbative mechanism of annihilation of fixed points between two and three dimensions. Secondly, we get a coherent picture of the physics of frustrated magnets in qualitative and (semi-) quantitative agreement with the numerical and experimental results. The central feature that emerges from our approach is the existence of scaling behaviors without fixed or pseudo-fixed point and that relies on a slowing-down of the renormalization group flow in a whole region in the coupling constants space. This phenomenon allows to explain the occurence of generic weak first order behaviors and to understand the absence of universality in the critical behavior of frustrated magnets.Comment: 58 pages, 15 PS figure

Laves intermetallics in stainless steel–zirconium alloys

Laves intermetallics have a significant effect on properties of metal waste forms being developed at Argonne National Laboratory. These waste forms are stainless steel-zirconium alloys that will contain radioactive metal isotopes isolated from spent nuclear fuel by electrometallurgical treatment. The baseline waste form composition for stainless steel-clad fuels is stainless steel-15 wt.% zirconium (SS-15Zr). This article presents results of neutron diffraction measurements, heat-treatment studies and mechanical testing on SS-15Zr alloys. The Laves intermetallics in these alloys, labeled Zr(Fe,Cr,Ni){sub 2+x}, have both C36 and C15 crystal structures. A fraction of these intermetallics transform into (Fe,Cr,Ni){sub 23}Zr{sub 6} during high-temperature annealing; the authors have proposed a mechanism for this transformation. The SS-15Zr alloys show virtually no elongation in uniaxial tension, but exhibit good strength and ductility in compression tests. This article also presents neutron diffraction and microstructural data for a stainless steel-42 wt.% zirconium (SS-42Zr) alloy