Reply to "Comment on Renormalization group picture of the Lifshitz critical behaviors"

We reply to a recent comment by Diehl and Shpot (cond-mat/0305131) criticizing a new approach to the Lifshitz critical behavior just presented (M. M. Leite Phys. Rev. B 67, 104415(2003)). We show that this approach is free of inconsistencies in the ultraviolet regime. We recall that the orthogonal approximation employed to solve arbitrary loop diagrams worked out at the criticized paper even at three-loop level is consistent with homogeneity for arbitrary loop momenta. We show that the criticism is incorrect.Comment: RevTex, 6 page

Exact renormalization group flow equations for non-relativistic fermions: scaling towards the Fermi surface

We construct exact functional renormalization group (RG) flow equations for non-relativistic fermions in arbitrary dimensions, taking into account not only mode elimination but also the rescaling of the momenta, frequencies and the fermionic fields. The complete RG flow of all relevant, marginal and irrelevant couplings can be described by a system of coupled flow equations for the irreducible n-point vertices. Introducing suitable dimensionless variables, we obtain flow equations for generalized scaling functions which are continuous functions of the flow parameter, even if we consider quantities which are dominated by momenta close to the Fermi surface, such as the density-density correlation function at long wavelengths. We also show how the problem of constructing the renormalized Fermi surface can be reduced to the problem of finding the RG fixed point of the irreducible two-point vertex at vanishing momentum and frequency. We argue that only if the degrees of freedom are properly rescaled it is possible to reach scale-invariant non-Fermi liquid fixed points within a truncation of the exact RG flow equations.Comment: 20 Revtex pages, with 4 figures; final version to appear in Phys. Rev. B; references and some explanations adde

Wegner-Houghton equation and derivative expansion

We study the derivative expansion for the effective action in the framework of the Exact Renormalization Group for a single component scalar theory. By truncating the expansion to the first two terms, the potential $U_k$ and the kinetic coefficient $Z_k$, our analysis suggests that a set of coupled differential equations for these two functions can be established under certain smoothness conditions for the background field and that sharp and smooth cut-off give the same result. In addition we find that, differently from the case of the potential, a further expansion is needed to obtain the differential equation for $Z_k$, according to the relative weight between the kinetic and the potential terms. As a result, two different approximations to the $Z_k$ equation are obtained. Finally a numerical analysis of the coupled equations for $U_k$ and $Z_k$ is performed at the non-gaussian fixed point in $D<4$ dimensions to determine the anomalous dimension of the field.Comment: 15 pages, 3 figure

The phase diagram of quantum systems: Heisenberg antiferromagnets

A novel approach for studying phase transitions in systems with quantum degrees of freedom is discussed. Starting from the microscopic hamiltonian of a quantum model, we first derive a set of exact differential equations for the free energy and the correlation functions describing the effects of fluctuations on the thermodynamics of the system. These equations reproduce the full renormalization group structure in the neighborhood of a critical point keeping, at the same time, full information on the non universal properties of the model. As a concrete application we investigate the phase diagram of a Heisenberg antiferromagnet in a staggered external magnetic field. At long wavelengths the known relationship to the Quantum Non Linear Sigma Model naturally emerges from our approach. By representing the two point function in an approximate analytical form, we obtain a closed partial differential equation which is then solved numerically. The results in three dimensions are in good agreement with available Quantum Monte Carlo simulations and series expansions. More refined approximations to the general framework presented here and few applications to other models are briefly discussed.Comment: 17 pages, 7 figure

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

Susceptibility amplitude ratio for generic competing systems

We calculate the susceptibility amplitude ratio near a generic higher character Lifshitz point up to one-loop order. We employ a renormalization group treatment with $L$ independent scaling transformations associated to the various inequivalent subspaces in the anisotropic case in order to compute the ratio above and below the critical temperature and demonstrate its universality. Furthermore, the isotropic results with only one type of competition axes have also been shown to be universal. We describe how the simpler situations of $m$-axial Lifshitz points as well as ordinary (noncompeting) systems can be retrieved from the present framework.Comment: 20 pages, no figure

Exact multilocal renormalization on the effective action : application to the random sine Gordon model statics and non-equilibrium dynamics

We extend the exact multilocal renormalization group (RG) method to study the flow of the effective action functional. This important physical quantity satisfies an exact RG equation which is then expanded in multilocal components. Integrating the nonlocal parts yields a closed exact RG equation for the local part, to a given order in the local part. The method is illustrated on the O(N) model by straightforwardly recovering the $\eta$ exponent and scaling functions. Then it is applied to study the glass phase of the Cardy-Ostlund, random phase sine Gordon model near the glass transition temperature. The static correlations and equilibrium dynamical exponent $z$ are recovered and several new results are obtained. The equilibrium two-point scaling functions are obtained. The nonequilibrium, finite momentum, two-time $t,t'$ response and correlations are computed. They are shown to exhibit scaling forms, characterized by novel exponents $\lambda_R \neq \lambda_C$, as well as universal scaling functions that we compute. The fluctuation dissipation ratio is found to be non trivial and of the form $X(q^z (t-t'), t/t')$. Analogies and differences with pure critical models are discussed.Comment: 33 pages, RevTe

Critical behavior at m-axial Lifshitz points: field-theory analysis and ϵ\epsilon-expansion results

The critical behavior of d-dimensional systems with an n-component order parameter is reconsidered at (m,d,n)-Lifshitz points, where a wave-vector instability occurs in an m-dimensional subspace of ${\mathbb R}^d$. Our aim is to sort out which ones of the previously published partly contradictory $\epsilon$-expansion results to second order in $\epsilon=4+\frac{m}{2}-d$ are correct. To this end, a field-theory calculation is performed directly in the position space of $d=4+\frac{m}{2}-\epsilon$ dimensions, using dimensional regularization and minimal subtraction of ultraviolet poles. The residua of the dimensionally regularized integrals that are required to determine the series expansions of the correlation exponents $\eta_{l2}$ and $\eta_{l4}$ and of the wave-vector exponent $\beta_q$ to order $\epsilon^2$ are reduced to single integrals, which for general m=1,...,d-1 can be computed numerically, and for special values of m, analytically. Our results are at variance with the original predictions for general m. For m=2 and m=6, we confirm the results of Sak and Grest [Phys. Rev. B {\bf 17}, 3602 (1978)] and Mergulh{\~a}o and Carneiro's recent field-theory analysis [Phys. Rev. B {\bf 59},13954 (1999)].Comment: Latex file with one figure (eps-file). Latex file uses texdraw to generate figures that are included in the tex

Applications of electrified dust and dust devil electrodynamics to Martian atmospheric electricity

Atmospheric transport and suspension of dust frequently brings electrification, which may be substantial. Electric fields of 10 kVm-1 to 100 kVm-1 have been observed at the surface beneath suspended dust in the terrestrial atmosphere, and some electrification has been observed to persist in dust at levels to 5 km, as well as in volcanic plumes. The interaction between individual particles which causes the electrification is incompletely understood, and multiple processes are thought to be acting. A variation in particle charge with particle size, and the effect of gravitational separation explains to, some extent, the charge structures observed in terrestrial dust storms. More extensive flow-based modelling demonstrates that bulk electric fields in excess of 10 kV m-1 can be obtained rapidly (in less than 10 s) from rotating dust systems (dust devils) and that terrestrial breakdown fields can be obtained. Modelled profiles of electrical conductivity in the Martian atmosphere suggest the possibility of dust electrification, and dust devils have been suggested as a mechanism of charge separation able to maintain current flow between one region of the atmosphere and another, through a global circuit. Fundamental new understanding of Martian atmospheric electricity will result from the ExoMars mission, which carries the DREAMS (Dust characterization, Risk Assessment, and Environment Analyser on the Martian Surface)-MicroARES (Atmospheric Radiation and Electricity Sensor) instrumentation to Mars in 2016 for the first in situ measurements

Energetic particle influence on the Earth's atmosphere

This manuscript gives an up-to-date and comprehensive overview of the effects of energetic particle precipitation (EPP) onto the whole atmosphere, from the lower thermosphere/mesosphere through the stratosphere and troposphere, to the surface. The paper summarizes the different sources and energies of particles, principally galactic cosmic rays (GCRs), solar energetic particles (SEPs) and energetic electron precipitation (EEP). All the proposed mechanisms by which EPP can affect the atmosphere are discussed, including chemical changes in the upper atmosphere and lower thermosphere, chemistry-dynamics feedbacks, the global electric circuit and cloud formation. The role of energetic particles in Earth’s atmosphere is a multi-disciplinary problem that requires expertise from a range of scientific backgrounds. To assist with this synergy, summary tables are provided, which are intended to evaluate the level of current knowledge of the effects of energetic particles on processes in the entire atmosphere