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

Topological Defects and the Spin Glass Phase of Cuprates

We propose that the spin glass phase of cuprates is due to the proliferation of topological defects of a spiral distortion of the antiferromagnet order. Our theory explains straightforwardly the simultaneous existence of short range incommensurate magnetic correlations and complete a-b symmetry breaking in this phase. We show via a renormalization group calculation that the collinear O(3)/O(2) symmetry is unstable towards the formation of local non-collinear correlations. A critical disorder strength is identified beyond which topological defects proliferate already at zero temperature.Comment: 7 pages, 2 figures. Final version with some changes and one replaced figur

Directional wave spectra observed during JONSWAP 1973

Estimates of the directional wave spectrum obtained from the meteorological buoy of the University of Hamburg and a pitch-and-roll buoy of the Institute of Oceanographic Sciences are reported from a series of measurements made within the framework of the Joint North Sea Wave Project during September 1973. Three main aspects were considered. First, the properties and parameterization of the directional spectrum were studied when the waves were generated by steady winds without any significant swell contribution. The results do not support the parameterization proposed by Mitsuyasu et al. (1975) and are in agreement with a parameterization in which the peak frequency is the relevant scale parameter. Second, comparisons are made between two independent methods of fitting the data exactly by means of a maximum likelihood technique (Long and Hasselmann, 1979) and a least-squares technique. The two methods give very similar fits to the observed data. Finally, the response of the directional wave spectrum to veering winds is considered and a simple model is constructed as a first attempt to describe some of the observations

Differential approximation for Kelvin-wave turbulence

I present a nonlinear differential equation model (DAM) for the spectrum of Kelvin waves on a thin vortex filament. This model preserves the original scaling of the six-wave kinetic equation, its direct and inverse cascade solutions, as well as the thermodynamic equilibrium spectra. Further, I extend DAM to include the effect of sound radiation by Kelvin waves. I show that, because of the phonon radiation, the turbulence spectrum ends at a maximum frequency $\omega^* \sim (\epsilon^3 c_s^{20} / \kappa^{16})^{1/13}$ where $\epsilon$ is the total energy injection rate, $c_s$ is the speed of sound and $\kappa$ is the quantum of circulation.Comment: Prepared of publication in JETP Letter

Dynamics of lattice pinned charge stripes

We study the transversal dynamics of a charged stripe (quantum string) and show that zero temperature quantum fluctuations are able to depin it from the lattice. If the hopping amplitude t is much smaller than the string tension J, the string is pinned by the underlying lattice. At t>>J, the string is depinned and allowed to move freely, if we neglect the effect of impurities. By mapping the system onto a 1D array of Josephson junctions, we show that the quantum depinning occurs at t/J = 2 / pi^2. Besides, we exploit the relation of the stripe Hamiltonian to the sine-Gordon theory and calculate the infrared excitation spectrum of the quantum string for arbitrary t/J values.Comment: 4 pages, 2 figure

Structural effect on the static spin and charge correlations in La1.875_{1.875}Ba0.125−x_{0.125-x}Srx_{x}CuO4_{4}

We report the results of elastic neutron scattering measurements performed on 1/8-hole doped La$_{1.875}$Ba$_{0.125-x}$Sr$_{x}$CuO$_{4}$ single crystals with {\it x}=0.05, 0.06, 0.075 and 0.085. In the low-temperature less-orthorhombic (LTLO, {\it Pccn} symmetry) phase, the charge-density-wave (CDW) and spin-density-wave (SDW) wavevectors were found to tilt in a low-symmetric direction with one-dimensional anisotropy in the CuO$_{2}$ plane, while they were aligned along the high-symmetry axis in the low-temperature tetragonal (LTT, {\it P}4$_2$/{\it ncm} symmetry) phase. The coincident direction of two wavevectors suggests a close relation between CDW and SDW orders. The SDW wavevector systematically deviates from the Cu-O bond direction in the LTLO phase upon Sr substitution and the tilt angle in the LTLO phase is smaller than that in the low-temperature orthorhombic phase (LTO, {\it B}{\it mab} symmetry) with comparable in-plane orthorhombic distortion. These results demonstrate a correlation between the corrugated pattern of CuO$_{2}$ plane and the deviations.Comment: 6 pages, 7figure

Signature of stripe pinning in optical conductivity

The response of charge stripes to an external electric field applied perpendicular to the stripe direction is studied within a diagrammatic approach for both weak and strong pinning by random impurities. The sound-like mode of the stripes described as elastic strings moves to finite frequency due to impurity pinning. By calculating the optical conductivity we determine this characteristic energy scale for both a single stripe and an array of interacting stripes. The results explain the anomalous far-infrared peak observed recently in optical-conductivity measurements on cuprates.Comment: Revised version, to appear in Phys. Rev.

Antiferromagnetic Ising spin glass competing with BCS pairing interaction in a transverse field

The competition among spin glass (SG), antiferromagnetism (AF) and local pairing superconductivity (PAIR) is studied in a two-sublattice fermionic Ising spin glass model with a local BCS pairing interaction in the presence of an applied magnetic transverse field $\Gamma$. In the present approach, spins in different sublattices interact with a Gaussian random coupling with an antiferromagnetic mean $J_0$ and standard deviation $J$. The problem is formulated in the path integral formalism in which spin operators are represented by bilinear combinations of Grassmann variables. The saddle-point Grand Canonical potential is obtained within the static approximation and the replica symmetric ansatz. The results are analysed in phase diagrams in which the AF and the SG phases can occur for small $g$ ($g$ is the strength of the local superconductor coupling written in units of $J$), while the PAIR phase appears as unique solution for large $g$. However, there is a complex line transition separating the PAIR phase from the others. It is second order at high temperature that ends in a tricritical point. The quantum fluctuations affect deeply the transition lines and the tricritical point due to the presence of $\Gamma$.Comment: 16 pages, 6 figures, accepted Eur. Phys. J.

Turbulence and particle acceleration in collisionless supernovae remnant shocks: II- Cosmic-ray transport

Supernovae remnant shock waves could be at the origin of cosmic rays up to energies in excess of the knee ($E\simeq3\cdot 10^{15}$eV) if the magnetic field is efficiently amplified by the streaming of accelerated particles in the shock precursor. This paper follows up on a previous paper \citep{pell05} which derived the properties of the MHD turbulence so generated, in particular its anisotropic character, its amplitude and its spectrum. In the present paper, we calculate the diffusion coefficients, also accounting for compression through the shock, and show that the predicted three-dimensional turbulence spectrum $k_\perp S_{3\rm d}(k_\parallel,k_\perp)\propto k_\parallel^{-1}k_\perp^{-\alpha}$ (with $k_\parallel$ and $k_\perp$ the wavenumber components along and perpendicular to the shock normal) generally leads to Bohm diffusion in the parallel direction. However, if the anisotropy is constrained by a relation of the form $k_\parallel \propto k_\perp^{2/3}$, which arises when the turbulent energy cascade occurs at a constant rate independent of scale, then the diffusion coefficient loses its Bohm scaling and scales as in isotropic Kolmogorov turbulence. We show that these diffusion coefficients allow to account for X-ray observations of supernova remnants. This paper also calculates the modification of the Fermi cycle due to the energy lost by cosmic rays in generating upstream turbulence and the concomittant steepening of the energy spectrum. Finally we confirm that cosmic rays can produced an amplified turbulence in young SNr during their free expansion phase such that the maximal energy is close to the knee and the spectral index is close to 2.3 in the warm phase of the interstellar mediumComment: 13 pages, 4 figures, accepted for publication in Astronomy & Astrophysics main journa