Nonequilibrium quantum phase transition in itinerant electron systems

We study the effect of the voltage bias on the ferromagnetic phase transition in a one-dimensional itinerant electron system. The applied voltage drives the system into a nonequilibrium steady state with a non-zero electric current. The bias changes the universality class of the second order ferromagnetic transition. While the equilibrium transition belongs to the universality class of the uniaxial ferroelectric, we find the mean-field behavior near the nonequilibrium critical point.Comment: Final version as accepted to Phys. Rev. Let

Destruction of bulk ordering by surface randomness

We demonstrate that the arbitrarily weak quenched disorder on the surface of a system of continuous symmetry destroys long range order in the bulk, and, instead, quasi-long range order emerges. Correlation functions are calculated exactly for the two- and three-dimensional XY model with surface randomness via the functional renormalization group. Even at strong quenched disorder the three-dimensional XY model possesses topological order. We also determine roughness of a domain wall in the presence of surface disorder.Comment: 4 pages Revtex; Eq. (12) correcte

Enhanced Peculiar Velocities in Brane-Induced Gravity

The mounting evidence for anomalously large peculiar velocities in our Universe presents a challenge for the LCDM paradigm. The recent estimates of the large scale bulk flow by Watkins et al. are inconsistent at the nearly 3 sigma level with LCDM predictions. Meanwhile, Lee and Komatsu have recently estimated that the occurrence of high-velocity merging systems such as the Bullet Cluster (1E0657-57) is unlikely at a 6.5-5.8 sigma level, with an estimated probability between 3.3x10^{-11} and 3.6x10^{-9} in LCDM cosmology. We show that these anomalies are alleviated in a broad class of infrared-modifed gravity theories, called brane-induced gravity, in which gravity becomes higher-dimensional at ultra large distances. These theories include additional scalar forces that enhance gravitational attraction and therefore speed up structure formation at late times and on sufficiently large scales. The peculiar velocities are enhanced by 24-34% compared to standard gravity, with the maximal enhancement nearly consistent at the 2 sigma level with bulk flow observations. The occurrence of the Bullet Cluster in these theories is 10^4 times more probable than in LCDM cosmology.Comment: 15 pages, 6 figures. v2: added reference

Quantum Bubble Nucleation beyond WKB: Resummation of Vacuum Bubble Diagrams

On the basis of Borel resummation, we propose a systematical improvement of bounce calculus of quantum bubble nucleation rate. We study a metastable super-renormalizable field theory, $D$ dimensional O(N) symmetric $\phi^4$ model ($D<4$) with an attractive interaction. The validity of our proposal is tested in D=1 (quantum mechanics) by using the perturbation series of ground state energy to high orders. We also present a result in D=2, based on an explicit calculation of vacuum bubble diagrams to five loop orders.Comment: 19 pages, 5 figures, PHYZZ

Quasi-long-range order in the random anisotropy Heisenberg model: functional renormalization group in 4-\epsilon dimensions

The large distance behaviors of the random field and random anisotropy O(N) models are studied with the functional renormalization group in 4-\epsilon dimensions. The random anisotropy Heisenberg (N=3) model is found to have a phase with the infinite correlation radius at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law < m(x) m(y) >\sim |x-y|^{-0.62\epsilon}. The magnetic susceptibility diverges at low fields as \chi \sim H^{-1+0.15\epsilon}. In the random field O(N) model the correlation radius is found to be finite at the arbitrarily weak disorder for any N>3. The random field case is studied with a new simple method, based on a rigorous inequality. This approach allows one to avoid the integration of the functional renormalization group equations.Comment: 12 pages, RevTeX; a minor change in the list of reference

Exact integral equation for the renormalized Fermi surface

The true Fermi surface of a fermionic many-body system can be viewed as a fixed point manifold of the renormalization group (RG). Within the framework of the exact functional RG we show that the fixed point condition implies an exact integral equation for the counterterm which is needed for a self-consistent calculation of the Fermi surface. In the simplest approximation, our integral equation reduces to the self-consistent Hartree-Fock equation for the counterterm.Comment: 5 pages, 1 figur

Critical Exponents of the N-vector model

Recently the series for two RG functions (corresponding to the anomalous dimensions of the fields phi and phi^2) of the 3D phi^4 field theory have been extended to next order (seven loops) by Murray and Nickel. We examine here the influence of these additional terms on the estimates of critical exponents of the N-vector model, using some new ideas in the context of the Borel summation techniques. The estimates have slightly changed, but remain within errors of the previous evaluation. Exponents like eta (related to the field anomalous dimension), which were poorly determined in the previous evaluation of Le Guillou--Zinn-Justin, have seen their apparent errors significantly decrease. More importantly, perhaps, summation errors are better determined. The change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values. Finally, because an error has been discovered in the last order of the published epsilon=4-d expansions (order epsilon^5), we have also reanalyzed the determination of exponents from the epsilon-expansion. The conclusion is that the general agreement between epsilon-expansion and 3D series has improved with respect to Le Guillou--Zinn-Justin.Comment: TeX Files, 27 pages +2 figures; Some values are changed; references update

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

The N-component Ginzburg-Landau Hamiltonian with cubic anisotropy: a six-loop study

We consider the Ginzburg-Landau Hamiltonian with a cubic-symmetric quartic interaction and compute the renormalization-group functions to six-loop order in d=3. We analyze the stability of the fixed points using a Borel transformation and a conformal mapping that takes into account the singularities of the Borel transform. We find that the cubic fixed point is stable for N>N_c, N_c = 2.89(4). Therefore, the critical properties of cubic ferromagnets are not described by the Heisenberg isotropic Hamiltonian, but instead by the cubic model at the cubic fixed point. For N=3, the critical exponents at the cubic and symmetric fixed points differ very little (less than the precision of our results, which is $\lesssim 1$ in the case of $\gamma$ and $\nu$). Moreover, the irrelevant interaction bringing from the symmetric to the cubic fixed point gives rise to slowly-decaying scaling corrections with exponent $\omega_2=0.010(4)$. For N=2, the isotropic fixed point is stable and the cubic interaction induces scaling corrections with exponent $\omega_2 = 0.103(8)$. These conclusions are confirmed by a similar analysis of the five-loop $\epsilon$-expansion. A constrained analysis which takes into account that $N_c = 2$ in two dimensions gives $N_c = 2.87(5)$.Comment: 29 pages, RevTex, new refs added, Phys. Rev. B in pres