Boundary critical behaviour at mm-axial Lifshitz points: the special transition for the case of a surface plane parallel to the modulation axes

The critical behaviour of $d$-dimensional semi-infinite systems with $n$-component order parameter $\bm{\phi}$ is studied at an $m$-axial bulk Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional subspace of $\mathbb{R}^d$. Field-theoretic renormalization group methods are utilised to examine the special surface transition in the case where the $m$ potential modulation axes, with $0\leq m\leq d-1$, are parallel to the surface. The resulting scaling laws for the surface critical indices are given. The surface critical exponent $\eta_\|^{\rm sp}$, the surface crossover exponent $\Phi$ and related ones are determined to first order in \epsilon=4+\case{m}{2}-d. Unlike the bulk critical exponents and the surface critical exponents of the ordinary transition, $\Phi$ is $m$-dependent already at first order in $\epsilon$. The \Or(\epsilon) term of $\eta_\|^{\rm sp}$ is found to vanish, which implies that the difference of $\beta_1^{\rm sp}$ and the bulk exponent $\beta$ is of order $\epsilon^2$.Comment: 21 pages, one figure included as eps file, uses IOP style file

Critical, crossover, and correction-to-scaling exponents for isotropic Lifshitz points to order (8−d)2\boldsymbol{(8-d)^2}

A two-loop renormalization group analysis of the critical behaviour at an isotropic Lifshitz point is presented. Using dimensional regularization and minimal subtraction of poles, we obtain the expansions of the critical exponents $\nu$ and $\eta$, the crossover exponent $\phi$, as well as the (related) wave-vector exponent $\beta_q$, and the correction-to-scaling exponent $\omega$ to second order in $\epsilon_8=8-d$. These are compared with the authors' recent $\epsilon$-expansion results [{\it Phys. Rev. B} {\bf 62} (2000) 12338; {\it Nucl. Phys. B} {\bf 612} (2001) 340] for the general case of an $m$-axial Lifshitz point. It is shown that the expansions obtained here by a direct calculation for the isotropic ($m=d$) Lifshitz point all follow from the latter upon setting $m=8-\epsilon_8$. This is so despite recent claims to the contrary by de Albuquerque and Leite [{\it J. Phys. A} {\bf 35} (2002) 1807].Comment: 11 pages, Latex, uses iop stylefiles, some graphs are generated automatically via texdra

Renormalized field theory and particle density profile in driven diffusive systems with open boundaries

We investigate the density profile in a driven diffusive system caused by a plane particle source perpendicular to the driving force. Focussing on the case of critical bulk density $\bar{c}$ we use a field theoretic renormalization group approach to calculate the density $c(z)$ as a function of the distance from the particle source at first order in $\epsilon=2-d$ ($d$: spatial dimension). For $d=1$ we find reasonable agreement with the exact solution recently obtained for the asymmetric exclusion model. Logarithmic corrections to the mean field profile are computed for $d=2$ with the result $c(z)-\bar{c} \sim z^{-1} (\ln(z))^{2/3}$ for $z \rightarrow \infty$.Comment: 32 pages, RevTex, 4 Postscript figures, to appear in Phys. Rev.

Surface critical behavior of driven diffusive systems with open boundaries

Using field theoretic renormalization group methods we study the critical behavior of a driven diffusive system near a boundary perpendicular to the driving force. The boundary acts as a particle reservoir which is necessary to maintain the critical particle density in the bulk. The scaling behavior of correlation and response functions is governed by a new exponent eta_1 which is related to the anomalous scaling dimension of the chemical potential of the boundary. The new exponent and a universal amplitude ratio for the density profile are calculated at first order in epsilon = 5-d. Some of our results are checked by computer simulations.Comment: 10 pages ReVTeX, 6 figures include

Crossover from Attractive to Repulsive Casimir Forces and Vice Versa

Systems described by an O(n) symmetrical $\phi^4$ Hamiltonian are considered in a $d$-dimensional film geometry at their bulk critical points. The critical Casimir forces between the film's boundary planes $\mathfrak{B}_j, j=1,2$, are investigated as functions of film thickness $L$ for generic symmetry-preserving boundary conditions $\partial_n\bm{\phi}=\mathring{c}_j\bm{\phi}$. The $L$-dependent part of the reduced excess free energy per cross-sectional area takes the scaling form $f_{\text{res}}\approx D(c_1L^{\Phi/\nu},c_2L^{\Phi/\nu})/L^{d-1}$ when $d<4$, where $c_i$ are scaling fields associated with the variables $\mathring{c}_i$, and $\Phi$ is a surface crossover exponent. Explicit two-loop renormalization group results for the function $D(\mathsf{c}_1,\mathsf{c}_2)$ at $d=4-\epsilon$ dimensions are presented. These show that (i) the Casimir force can have either sign, depending on $\mathsf{c}_1$ and $\mathsf{c}_2$, and (ii) for appropriate choices of the enhancements $\mathring{c}_j$, crossovers from attraction to repulsion and vice versa occur as $L$ increases.Comment: 4 RevTeX pages, 2 eps figures; minor misprints corrected and 3 references adde

Effects of surfaces on resistor percolation

We study the effects of surfaces on resistor percolation at the instance of a semi-infinite geometry. Particularly we are interested in the average resistance between two connected ports located on the surface. Based on general grounds as symmetries and relevance we introduce a field theoretic Hamiltonian for semi-infinite random resistor networks. We show that the surface contributes to the average resistance only in terms of corrections to scaling. These corrections are governed by surface resistance exponents. We carry out renormalization group improved perturbation calculations for the special and the ordinary transition. We calculate the surface resistance exponents \phi_{\mathcal S \mathnormal} and \phi_{\mathcal S \mathnormal}^\infty for the special and the ordinary transition, respectively, to one-loop order.Comment: 19 pages, 3 figure

Probing the evolving massive star population in Orion with kinematic and radioactive tracers

We assemble a census of the most massive stars in Orion, then use stellar isochrones to estimate their masses and ages, and use these results to establish the stellar content of Orion's individual OB associations. From this, our new population synthesis code is utilized to derive the history of the emission of UV radiation and kinetic energy of the material ejected by the massive stars, and also follow the ejection of the long-lived radioactive isotopes 26Al and 60Fe. In order to estimate the precision of our method, we compare and contrast three distinct representations of the massive stars. We compare the expected outputs with observations of 26Al gamma-ray signal and the extent of the Eridanus cavity. We find an integrated kinetic energy emitted by the massive stars of 1.8(+1.5-0.4)times 10^52 erg. This number is consistent with the energy thought to be required to create the Eridanus superbubble. We also find good agreement between our model and the observed 26Al signal, estimating a mass of 5.8(+2.7-2.5) times 10^-4 Msol of 26Al in the Orion region. Our population synthesis approach is demonstrated for the Orion region to reproduce three different kinds of observable outputs from massive stars in a consistent manner: Kinetic energy as manifested in ISM excavation, ionization as manifested in free-free emission, and nucleosynthesis ejecta as manifested in radioactivity gamma-rays. The good match between our model and the observables does not argue for considerable modifications of mass loss. If clumping effects turn out to be strong, other processes would need to be identified to compensate for their impact on massive-star outputs. Our population synthesis analysis jointly treats kinematic output and the return of radioactive isotopes, which proves a powerful extension of the methodology that constrains feedback from massive stars.Comment: Accepted for publication in A&A, 10 page

Comment on `Renormalization-Group Calculation of the Dependence on Gravity of the Surface Tension and Bending Rigidity of a Fluid Interface'

It is shown that the interface model introduced in Phys. Rev. Lett. 86, 2369 (2001) violates fundamental symmetry requirements for vanishing gravitational acceleration $g$, so that its results cannot be applied to critical properties of interfaces for $g\to 0$.Comment: A Comment on a recent Letter by J.G. Segovia-L\'opez and V. Romero-Roch\'{\i}n, Phys. Rev. Lett.86, 2369 (2001). Latex file, 1 page (revtex

Self-affine surface morphology of plastically deformed metals

We analyze the surface morphology of metals after plastic deformation over a range of scales from 10 nm to 2 mm, using a combination of atomic force microscopy and scanning white-light interferometry. We demonstrate that an initially smooth surface during deformation develops self-affine roughness over almost four orders of magnitude in scale. The Hurst exponent $H$ of one-dimensional surface profiles is initially found to decrease with increasing strain and then stabilizes at $H \approx 0.75$. By analyzing their statistical properties we show that the one-dimensional surface profiles can be mathematically modelled as graphs of a fractional Brownian motion. Our findings can be understood in terms of a fractal distribution of plastic strain within the deformed samples