Boundary critical behavior at m-axial Lifshitz points for a boundary plane parallel to the modulation axes

The critical behavior of semi-infinite $d$-dimensional systems with $n$-component order parameter $\bm{\phi}$ and short-range interactions is investigated at an $m$-axial bulk Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional subspace of $\mathbb{R}^d$. The associated $m$ modulation axes are presumed to be parallel to the surface, where $0\le m\le d-1$. An appropriate semi-infinite $|\bm{\phi}|^4$ model representing the corresponding universality classes of surface critical behavior is introduced. It is shown that the usual O(n) symmetric boundary term $\propto \bm{\phi}^2$ of the Hamiltonian must be supplemented by one of the form $\mathring{\lambda} \sum_{\alpha=1}^m(\partial\bm{\phi}/\partial x_\alpha)^2$ involving a dimensionless (renormalized) coupling constant $\lambda$. The implied boundary conditions are given, and the general form of the field-theoretic renormalization of the model below the upper critical dimension $d^*(m)=4+{m}/{2}$ is clarified. Fixed points describing the ordinary, special, and extraordinary transitions are identified and shown to be located at a nontrivial value $\lambda^*$ if $\epsilon\equiv d^*(m)-d>0$. The surface critical exponents of the ordinary transition are determined to second order in $\epsilon$. Extrapolations of these $\epsilon$ expansions yield values of these exponents for $d=3$ in good agreement with recent Monte Carlo results for the case of a uniaxial ($m=1$) Lifshitz point. The scaling dimension of the surface energy density is shown to be given exactly by $d+m (\theta-1)$, where $\theta=\nu_{l4}/\nu_{l2}$ is the anisotropy exponent.Comment: revtex4, 31 pages with eps-files for figures, uses texdraw to generate some graphs; to appear in PRB; v2: some references and additional remarks added, labeling in figure 1 and some typos correcte

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

Dynamic surface scaling behavior of isotropic Heisenberg ferromagnets

The effects of free surfaces on the dynamic critical behavior of isotropic Heisenberg ferromagnets are studied via phenomenological scaling theory, field-theoretic renormalization group tools, and high-precision computer simulations. An appropriate semi-infinite extension of the stochastic model J is constructed, the boundary terms of the associated dynamic field theory are identified, its renormalization in d <= 6 dimensions is clarified, and the boundary conditions it satisfies are given. Scaling laws are derived which relate the critical indices of the dynamic and static infrared singularities of surface quantities to familiar static bulk and surface exponents. Accurate computer-simulation data are presented for the dynamic surface structure factor; these are in conformity with the predicted scaling behavior and could be checked by appropriate scattering experiments.Comment: 9 pages, 2 figure

Analytic Solution of Emden-Fowler Equation and Critical Adsorption in Spherical Geometry

In the framework of mean-field theory the equation for the order-parameter profile in a spherically-symmetric geometry at the bulk critical point reduces to an Emden-Fowler problem. We obtain analytic solutions for the surface universality class of extraordinary transitions in $d=4$ for a spherical shell, which may serve as a starting point for a pertubative calculation. It is demonstrated that the solution correctly reproduces the Fisher-de Gennes effect in the limit of the parallel-plate geometry.Comment: (to be published in Z. Phys. B), 7 pages, 1 figure, uuencoded postscript file, 8-9

Critical Casimir amplitudes for nn-component ϕ4\phi^4 models with O(n)-symmetry breaking quadratic boundary terms

Euclidean $n$-component $\phi^4$ theories whose Hamiltonians are O(n) symmetric except for quadratic symmetry breaking boundary terms are studied in films of thickness $L$. The boundary terms imply the Robin boundary conditions $\partial_n\phi_\alpha =\mathring{c}^{(j)}_\alpha \phi_\alpha$ at the boundary planes $\mathfrak{B}_{j=1,2}$ at $z=0$ and $z=L$. Particular attention is paid to the cases in which $m_j$ of the $n$ variables $\mathring{c}^{(j)}_\alpha$ take the special value $\mathring{c}_{m_j\text{-sp}}$ corresponding to critical enhancement while the remaining ones are subcritically enhanced. Under these conditions, the semi-infinite system bounded by $\mathfrak{B}_j$ has a multicritical point, called $m_j$-special, at which an $O(m_j)$ symmetric critical surface phase coexists with the O(n) symmetric bulk phase, provided $d$ is sufficiently large. The $L$-dependent part of the reduced free energy per area behaves as $\Delta_C/L^{d-1}$ as $L\to\infty$ at the bulk critical point. The Casimir amplitudes $\Delta_C$ are determined for small $\epsilon=4-d$ in the general case where $m_{c,c}$ components $\phi_\alpha$ are critically enhanced at both boundary planes, $m_{c,D} + m_{D,c}$ components are enhanced at one plane but satisfy asymptotic Dirichlet boundary conditions at the respective other, and the remaining $m_{D,D}$ components satisfy asymptotic Dirichlet boundary conditions at both $\mathfrak{B}_j$. Whenever $m_{c,c}>0$, these expansions involve integer and fractional powers $\epsilon^{k/2}$ with $k\ge 3$ (mod logarithms). Results to $O(\epsilon^{3/2})$ for general values of $m_{c,c}$, $m_{c,D}+m_{D,c}$, and $m_{D,D}$ are used to estimate the $\Delta_C$ of 3D Heisenberg systems with surface spin anisotropies when $(m_{c,c}, m_{c,D}+ m_{D,c}) = (1,0)$, $(0,1)$, and $(1,1)$.Comment: Latex source file with 5 eps files; version with minor amendments and corrected typo

Proton-Antiproton Annihilation into a Lambda_c-Antilambda_c Pair

The process p-pbar -> Lambda_c-Antilambda_c is investigated within the handbag approach. It is shown that the dominant dynamical mechanism, characterized by the partonic subprocess u-ubar -> c-cbar factorizes in the sense that only the subprocess contains highly virtual partons, a gluon to lowest order of perturbative QCD, while the hadronic matrix elements embody only soft scales and can be parameterized in terms of helicity flip and non-flip generalized parton distributions. Modelling these parton distributions by overlaps of light-cone wave functions for the involved baryons we are able to predict cross sections and spin correlation parameters for the process of interest.Comment: 39 pages, 7 figures, problems with printout of figures resolved, Ref. 33 and referring sentences in section 4 change

Surface critical exponents at a uniaxial Lifshitz point

Using Monte Carlo techniques, the surface critical behaviour of three-dimensional semi-infinite ANNNI models with different surface orientations with respect to the axis of competing interactions is investigated. Special attention is thereby paid to the surface criticality at the bulk uniaxial Lifshitz point encountered in this model. The presented Monte Carlo results show that the mean-field description of semi-infinite ANNNI models is qualitatively correct. Lifshitz point surface critical exponents at the ordinary transition are found to depend on the surface orientation. At the special transition point, however, no clear dependency of the critical exponents on the surface orientation is revealed. The values of the surface critical exponents presented in this study are the first estimates available beyond mean-field theory.Comment: 10 pages, 7 figures include

Massive Field-Theory Approach to Surface Critical Behavior in Three-Dimensional Systems

The massive field-theory approach for studying critical behavior in fixed space dimensions $d<4$ is extended to systems with surfaces.This enables one to study surface critical behavior directly in dimensions $d<4$ without having to resort to the $\epsilon$ expansion. The approach is elaborated for the representative case of the semi-infinite |\bbox{\phi}|^4 $n$-vector model with a boundary term {1/2} c_0\int_{\partial V}\bbox{\phi}^2 in the action. To make the theory uv finite in bulk dimensions $3\le d<4$, a renormalization of the surface enhancement $c_0$ is required in addition to the standard mass renormalization. Adequate normalization conditions for the renormalized theory are given. This theory involves two mass parameter: the usual bulk `mass' (inverse correlation length) $m$, and the renormalized surface enhancement $c$. Thus the surface renormalization factors depend on the renormalized coupling constant $u$ and the ratio $c/m$. The special and ordinary surface transitions correspond to the limits $m\to 0$ with $c/m\to 0$ and $c/m\to\infty$, respectively. It is shown that the surface-enhancement renormalization turns into an additive renormalization in the limit $c/m\to\infty$. The renormalization factors and exponent functions with $c/m=0$ and $c/m=\infty$ that are needed to determine the surface critical exponents of the special and ordinary transitions are calculated to two-loop order. The associated series expansions are analyzed by Pad\'e-Borel summation techniques. The resulting numerical estimates for the surface critical exponents are in good agreement with recent Monte Carlo simulations. This also holds for the surface crossover exponent $\Phi$.Comment: Revtex, 40 pages, 3 figures, and 8 pictograms (included in equations

Relativistic Quantum Gravity at a Lifshitz Point

We show that the Horava theory for the completion of General Relativity at UV scales can be interpreted as a gauge fixed theory, and it can be extended to an invariant theory under the full group of four-dimensional diffeomorphisms. In this respect, although being fully relativistic, it results to be locally anisotropic in the time-like and space-like directions defined by a family of irrotational observers. We show that this theory propagates generically three degrees of freedom: two of them are related to the four-dimensional diffeomorphism invariant graviton (the metric) and one is related to a propagating scalar mode. Finally, we note that in the present formulation, matter can be consistently coupled to gravity.Comment: v4: Erratum added: explanation on the true dynamical fields of the relativistic theory added. The theory is interpreted as a Tensor-Scalar relativistic theory. Reference added. Version accepted in JHE

Dynamical Relaxation and Universal Short-Time Behavior in Finite Systems: The Renormalization Group Approach

We study how the finite-sized n-component model A with periodic boundary conditions relaxes near its bulk critical point from an initial nonequilibrium state with short-range correlations. Particular attention is paid to the universal long-time traces that the initial condition leaves. An approach based on renormalization-group improved perturbation theory in 4-epsilon space dimensions and a nonperturbative treatment of the q=0 mode of the fluctuating order-parameter field is developed. This leads to a renormalized effective stochastic equation for this mode in the background of the other q=0 modes; we explicitly derive it to one-loop order, show that it takes the expected finite-size scaling form at the fixed point, and solve it numerically. Our results confirm for general n that the amplitude of the magnetization density m(t) in the linear relaxation-time regime depends on the initial magnetization in the universal fashion originally found in our large-$n$ analysis [J.\ Stat. Phys. 73 (1993) 1]. The anomalous short-time power-law increase of m(t) also is recovered. For n=1, our results are in fair agreement with recent Monte Carlo simulations by Li, Ritschel, and Zheng [J. Phys. A 27 (1994) L837] for the three-dimensional Ising model.Comment: 27 pages, 7 postscript figures, REVTEX 3.0, submitted to Nucl. Phys.