Harmonic crossover exponents in O(n) models with the pseudo-epsilon expansion approach

We determine the crossover exponents associated with the traceless tensorial quadratic field, the third- and fourth-harmonic operators for O(n) vector models by re-analyzing the existing six-loop fixed dimension series with pseudo-epsilon expansion. Within this approach we obtain the most accurate theoretical estimates that are in optimum agreement with other theoretical and experimental results.Comment: 12 pages, 1 figure. Final version accepted for publicatio

Dimensional crossover in dipolar magnetic layers

We investigate the static critical behaviour of a uniaxial magnetic layer, with finite thickness L in one direction, yet infinitely extended in the remaining d dimensions. The magnetic dipole-dipole interaction is taken into account. We apply a variant of Wilson's momentum shell renormalisation group approach to describe the crossover between the critical behaviour of the 3-D Ising, 2-d Ising, 3-D uniaxial dipolar, and the 2-d uniaxial dipolar universality classes. The corresponding renormalisation group fixed points are in addition to different effective dimensionalities characterised by distinct analytic structures of the propagator, and are consequently associated with varying upper critical dimensions. While the limiting cases can be discussed by means of dimensional epsilon expansions with respect to the appropriate upper critical dimensions, respectively, the crossover features must be addressed in terms of the renormalisation group flow trajectories at fixed dimensionality d.Comment: 25 pages, Latex, 12 figures (.eps files) and IOP style files include

From neurons to epidemics: How trophic coherence affects spreading processes

Trophic coherence, a measure of the extent to which the nodes of a directed network are organised in levels, has recently been shown to be closely related to many structural and dynamical aspects of complex systems, including graph eigenspectra, the prevalence or absence of feed-back cycles, and linear stability. Furthermore, non-trivial trophic structures have been observed in networks of neurons, species, genes, metabolites, cellular signalling, concatenated words, P2P users, and world trade. Here we consider two simple yet apparently quite different dynamical models -- one a Susceptible-Infected-Susceptible (SIS) epidemic model adapted to include complex contagion, the other an Amari-Hopfield neural network -- and show that in both cases the related spreading processes are modulated in similar ways by the trophic coherence of the underlying networks. To do this, we propose a network assembly model which can generate structures with tunable trophic coherence, limiting in either perfectly stratified networks or random graphs. We find that trophic coherence can exert a qualitative change in spreading behaviour, determining whether a pulse of activity will percolate through the entire network or remain confined to a subset of nodes, and whether such activity will quickly die out or endure indefinitely. These results could be important for our understanding of phenomena such as epidemics, rumours, shocks to ecosystems, neuronal avalanches, and many other spreading processes

Influence of Basis-set Size on the X\u3csup\u3e2\u3c/sup\u3eΣ\u3csup\u3e+\u3c/sup\u3e\u3csub\u3e1/2\u3c/sub\u3e, A\u3csup\u3e2\u3c/sup\u3eΠ\u3csub\u3e1/2\u3c/sub\u3e, A\u3csup\u3e2\u3c/sup\u3eΠ\u3csub\u3e3/2\u3c/sub\u3e, and B\u3csup\u3e2\u3c/sup\u3eΣ\u3csub\u3e1/2\u3c/sub\u3e potential-energy curves, A\u3csup\u3e2\u3c/sup\u3eΠ\u3csub\u3e3/2\u3c/sub\u3e 2 vibrational energies, and D\u3csub\u3e1\u3c/sub\u3e and D\u3csub\u3e2\u3c/sub\u3e line shapes of Rb+He

The X 2 Σ + 1 / 2 , A 2 Π 1 / 2 , A 2 Π 3 / 2 , and B 2 Σ + 1 / 2 potential-energy curves for Rb+He are computed at the spin-orbit multireference configuration interaction level of theory using a hierarchy of Gaussian basis sets at the double-zeta (DZ), triple-zeta (TZ), and quadruple-zeta (QZ) levels of valence quality. Counterpoise and Davidson-Silver corrections are employed to remove basis-set superposition error and ameliorate size-consistency error. An extrapolation is performed to obtain a final set of potential-energy curves in the complete basis-set (CBS) limit. This yields four sets of systematically improved X 2 Σ + 1 / 2 , A 2 Π 1 / 2 , A 2 Π 3 / 2 , and B 2 Σ + 1 / 2 potential-energy curves that are used to compute the A 2 Π 3 / 2 bound vibrational energies, the position of the D 2 blue satellite peak, and the D 1 and D 2 pressure broadening and shifting coefficients, at the DZ, TZ, QZ, and CBS levels. Results are compared with previous calculations and experimental observation

"Double-trace" Deformations, Boundary Conditions and Spacetime Singularities

Double-trace deformations of the AdS/CFT duality result in a new perturbation expansion for string theory, based on a non-local worldsheet. We discuss some aspects of the deformation in the low energy gravity approximation, where it appears as a change in the boundary condition of fields. We relate unique features of the boundary of AdS to the worldsheet becoming non-local, and conjecture that non-local worldsheet actions may be generic in other classes of backgrounds.Comment: 21 pages, 2 figures, harvmac. v2: minor changes, references added, version sent to JHEP. v3 minor correction

Quantum anomaly, universal relations, and breathing mode of a two-dimensional Fermi gas

In this Letter, we show that the classical SO(2,1) symmetry of a harmonically trapped Fermi gas in two dimensions is broken by quantum effects. The anomalous correction to the symmetry algebra is given by a two-body operator that is well known as the contact. Taking into account this modification, we are able to derive the virial theorem for the system and a universal relation for the pressure of a homogeneous gas. The existence of an undamped breathing mode is associated with the classical symmetry. We provide an estimate for the anomalous frequency shift of this oscillation at zero temperature and compare the result with a recent experiment by [E. Vogt et al., Phys. Rev. Lett. 108, 070404 (2012)]. Discrepancies are attributed to finite temperature effects.Comment: 5 pages, 1 figure; v3: published versio

Stability Analysis of Asynchronous States in Neuronal Networks with Conductance-Based Inhibition

Oscillations in networks of inhibitory interneurons have been reported at various sites of the brain and are thought to play a fundamental role in neuronal processing. This Letter provides a self-contained analytical framework that allows numerically efficient calculations of the population activity of a network of conductance-based integrate-and-fire neurons that are coupled through inhibitory synapses. Based on a normalization equation this Letter introduces a novel stability criterion for a network state of asynchronous activity and discusses its perturbations. The analysis shows that, although often neglected, the reversal potential of synaptic inhibition has a strong influence on the stability as well as the frequency of network oscillations

Gpr126/Adgrg6 has Schwann cell autonomous and nonautonomous functions in peripheral nerve injury and repair

Schwann cells (SCs) are essential for proper peripheral nerve development and repair, although the mechanisms regulating these processes are incompletely understood. We previously showed that the adhesion G protein-coupled receptor Gpr126/Adgrg6 is essential for SC development and myelination. Interestingly, the expression of Gpr126 is maintained in adult SCs, suggestive of a function in the mature nerve. We therefore investigated the role of Gpr126 in nerve repair by studying an inducible SC-specific Gpr126 knock-out mouse model. Here, we show that remyelination is severely delayed after nerve-crush injury. Moreover, we also observe noncell-autonomous defects in macrophage recruitment and axon regeneration in injured nerves following loss of Gpr126 in SCs. This work demonstrates that Gpr126 has critical SC-autonomous and SC-nonautonomous functions in remyelination and peripheral nerve repair. SIGNIFICANCE STATEMENT Lack of robust remyelination represents one of the major barriers to recovery of neurological functions in disease or following injury in many disorders of the nervous system. Here we show that the adhesion class G protein-coupled receptor (GPCR) Gpr126/Adgrg6 is required for remyelination, macrophage recruitment, and axon regeneration following nerve injury. At least 30% of all approved drugs target GPCRs; thus, Gpr126 represents an attractive potential target to stimulate repair in myelin disease or following nerve injury

Spin Glass and ferromagnetism in disordered Cerium compounds

The competition between spin glass, ferromagnetism and Kondo effect is analysed here in a Kondo lattice model with an inter-site random coupling $J_{ij}$ between the localized magnetic moments given by a generalization of the Mattis model which represents an interpolation between ferromagnetism and a highly disordered spin glass. Functional integral techniques with Grassmann fields have been used to obtain the partition function. The static approximation and the replica symmetric ansatz have also been used. The solution of the problem is presented as a phase diagram giving $T/{J}$ {\it versus} $J_K/J$ where $T$ is the temperature, $J_{K}$ and ${J}$ are the strengths of the intrasite Kondo and the intersite random couplings, respectively. If $J_K/{J}$ is small, when temperature is decreased, there is a second order transition from a paramagnetic to a spin glass phase. For lower $T/{J}$, a first order transition appears between the spin glass phase and a region where there are Mattis states which are thermodynamically equivalent to the ferromagnetism. For very low ${T/{J}}$, the Mattis states become stable. On the other hand, it is found as solution a Kondo state for large $J_{K}/{J}$ values. These results can improve the theoretical description of the well known experimental phase diagram of $CeNi_{1-x}Cu_{x}$.Comment: 17 pages, 5 figures, accepted Phys. Rev.