Spectral Renormalization Group for the Gaussian model and ψ4\psi^4 theory on non-spatial networks

We implement the spectral renormalization group on different deterministic non-spatial networks without translational invariance. We calculate the thermodynamic critical exponents for the Gaussian model on the Cayley tree and the diamond lattice, and find that they are functions of the spectral dimension, $\tilde{d}$. The results are shown to be consistent with those from exact summation and finite size scaling approaches. At $\tilde{d}=2$, the lower critical dimension for the Ising universality class, the Gaussian fixed point is stable with respect to a $\psi^4$ perturbation up to second order. However, on generalized diamond lattices, non-Gaussian fixed points arise for $2<\tilde{d}<4$.Comment: 16 pages, 14 figures, 5 tables. The paper has been extended to include a $\psi^4$ interactions and higher spectral dimension

Algorithmic correspondence and completeness in modal logic. I. The core algorithm SQEMA

Modal formulae express monadic second-order properties on Kripke frames, but in many important cases these have first-order equivalents. Computing such equivalents is important for both logical and computational reasons. On the other hand, canonicity of modal formulae is important, too, because it implies frame-completeness of logics axiomatized with canonical formulae. Computing a first-order equivalent of a modal formula amounts to elimination of second-order quantifiers. Two algorithms have been developed for second-order quantifier elimination: SCAN, based on constraint resolution, and DLS, based on a logical equivalence established by Ackermann. In this paper we introduce a new algorithm, SQEMA, for computing first-order equivalents (using a modal version of Ackermann's lemma) and, moreover, for proving canonicity of modal formulae. Unlike SCAN and DLS, it works directly on modal formulae, thus avoiding Skolemization and the subsequent problem of unskolemization. We present the core algorithm and illustrate it with some examples. We then prove its correctness and the canonicity of all formulae on which the algorithm succeeds. We show that it succeeds not only on all Sahlqvist formulae, but also on the larger class of inductive formulae, introduced in our earlier papers. Thus, we develop a purely algorithmic approach to proving canonical completeness in modal logic and, in particular, establish one of the most general completeness results in modal logic so far.Comment: 26 pages, no figures, to appear in the Logical Methods in Computer Scienc

Cluster diagonalization in systematically expanded Hilbert spaces: application to models of correlated electrons

A method of cluster diagonalization in a systematically expanded Hilbert space is described. We discuss some applications of this procedure to models of high-T_c superconductors, like the t - J and one and three bands Hubbard models in two dimensions. The results obtained with this method are compared against results obtained with other techniques dealing with truncated Hilbert spaces. The relation between this method of diagonalization in a reduced Hilbert space, and perturbation theory and variational techniques is also discussed.Comment: 26 pages + 12 figures, available upon request, LATEX, preprint ORNL/CCIP/93/

Fermion-scalar interactions with domain wall fermions

Domain wall fermions are defined on a lattice with an extra direction the size of which controls the chiral properties of the theory. When gauge fields are coupled to domain wall fermions the extra direction is treated as an internal flavor space. Here it is found that this is not the case for scalar fields. Instead, the interaction takes place only along the link that connects the boundaries of the extra direction. This reveals a richness in the way different spin particles are coupled to domain wall fermions. As an application, 4-Fermi models are studied using large N techniques and the results are supported by numerical simulations with N=2. It is found that the chiral properties of domain wall fermions in these models are good across a large range of couplings and that a phase with parity-flavor broken symmetry can develop for negative bare masses if the number of sites along the extra direction is finite.Comment: LaTeX, 17 pages, 8 eps figures; comment regarding the width of Aoki phase added in sec. 3; references adde

Finite volume schemes for diffusion equations: introduction to and review of modern methods

We present Finite Volume methods for diffusion equations on generic meshes, that received important coverage in the last decade or so. After introducing the main ideas and construction principles of the methods, we review some literature results, focusing on two important properties of schemes (discrete versions of well-known properties of the continuous equation): coercivity and minimum-maximum principles. Coercivity ensures the stability of the method as well as its convergence under assumptions compatible with real-world applications, whereas minimum-maximum principles are crucial in case of strong anisotropy to obtain physically meaningful approximate solutions

Fast and automated oscillation frequency extraction using Bayesian multi-modality

Since the advent of CoRoT, and NASA Kepler and K2, the number of low- and intermediate-mass stars classified as pulsators has increased very rapidly with time, now accounting for several $10^4$ targets. With the recent launch of NASA TESS space mission, we have confirmed our entrance to the era of all-sky observations of oscillating stars. TESS is currently releasing good quality datasets that already allow for the characterization and identification of individual oscillation modes even from single 27-days shots on some stars. When ESA PLATO will become operative by the next decade, we will face the observation of several more hundred thousands stars where identifying individual oscillation modes will be possible. However, estimating the individual frequency, amplitude, and lifetime of the oscillation modes is not an easy task. This is because solar-like oscillations and especially their evolved version, the red giant branch (RGB) oscillations, can vary significantly from one star to another depending on its specific stage of the evolution, mass, effective temperature, metallicity, as well as on its level of rotation and magnetism. In this perspective I will present a novel, fast, and powerful way to derive individual oscillation mode frequencies by building on previous results obtained with \diamonds. I will show that the oscillation frequencies obtained with this new approach can reach precisions of about 0.1 % and accuracies of about 0.01 % when compared to published literature values for the RGB star KIC~12008916.Comment: 10 pages, 2 figures, accepted for publication in Frontiers in Astronomy and Space Sciences. Invited contribution for the research topic "The Future of Asteroseismology

Cold Dark Matter Substructure and Galactic Disks

We perform a set of high-resolution, dissipationless N-body simulations to investigate the influence of cold dark matter (CDM) substructure on the dynamical evolution of thin galactic disks. Our method combines cosmological simulations of galaxy-sized CDM halos to derive the properties of substructure populations and controlled numerical experiments of consecutive subhalo impacts onto initially-thin, fully-formed disk galaxies. We demonstrate that close encounters between massive subhalos and galactic disks since z~1 should be common occurrences in LCDM models. In contrast, extremely few satellites in present-day CDM halos are likely to have a significant impact on the disk structure. One typical host halo merger history is used to seed controlled N-body experiments of subhalo-disk encounters. As a result of these accretion events, the disk thickens considerably at all radii with the disk scale height increasing in excess of a factor of 2 in the solar neighborhood. We show that interactions with the subhalo population produce a wealth of distinctive morphological signatures in the disk stars including: conspicuous flares; bars; low-lived, ring-like features in the outskirts; and low-density, filamentary structures above the disk plane. We compare a resulting dynamically-cold, ring-like feature in our simulations to the Monoceros ring stellar structure in the MW. The comparison shows quantitative agreement in both spatial distribution and kinematics, suggesting that such observed complex stellar components may arise naturally as disk stars are excited by encounters with subhalos. These findings highlight the significant role of CDM substructure in setting the structure of disk galaxies and driving galaxy evolution.Comment: 10 pages, 4 figures. To appear in the proceedings of the IAU Symposium No. 254 "The Galaxy Disk in Cosmological Context", Copenhagen 9-13 June 2008, Denmark, (Eds.) J. Andersen, J. Bland-Hawthorn & B. Nordstrom, Cambridge University Pres

Effect of electron-phonon interaction range on lattice polaron dynamics: a continuous-time quantum Monte Carlo study

We present the numerically exact ground state energy, effective mass, and isotope exponents of a one-dimensional lattice polaron, valid for any range of electron-phonon interaction, applying a new continuous-time Quantum Monte Carlo (QMC) technique in a wide range of coupling strength and adiabatic ratio. The QMC method is free from any systematic finite-size and finite-time-step errors. We compare our numerically exact results with analytical weak-coupling theory and with the strong-coupling $1/\lambda$ expansion. We show that the exact results agree well with the canonical Fr\"ohlich and Holstein-Lang-Firsov theories in the weak and strong coupling limits, respectively, for any range of interaction. We find a strong dependence of the polaron dynamics on the range of interaction. An increased range of interaction has a similar effect to an increased (less adiabatic) phonon frequency: specifically, a reduction in the effective mass.Comment: 27 pages, 16 figures, to appear Phys Rev B. Introduction rewritten, comparison with other authors extended, description of method shortened, improved treatment of weak coupling theor

Universal Reduction of Effective Coordination Number in the Quasi-One-Dimensional Ising Model

Critical temperature of quasi-one-dimensional general-spin Ising ferromagnets is investigated by means of the cluster Monte Carlo method performed on infinite-length strips, L times infty or L times L times infty. We find that in the weak interchain coupling regime the critical temperature as a function of the interchain coupling is well-described by a chain mean-field formula with a reduced effective coordination number, as the quantum Heisenberg antiferromagnets recently reported by Yasuda et al. [Phys. Rev. Lett. 94, 217201 (2005)]. It is also confirmed that the effective coordination number is independent of the spin size. We show that in the weak interchain coupling limit the effective coordination number is, irrespective of the spin size, rigorously given by the quantum critical point of a spin-1/2 transverse-field Ising model.Comment: 12 pages, 6 figures, minor modifications, final version published in Phys. Rev.