Zeros of the Partition Function for Higher--Spin 2D Ising Models

We present calculations of the complex-temperature zeros of the partition functions for 2D Ising models on the square lattice with spin $s=1$, 3/2, and 2. These give insight into complex-temperature phase diagrams of these models in the thermodynamic limit. Support is adduced for a conjecture that all divergences of the magnetisation occur at endpoints of arcs of zeros protruding into the FM phase. We conjecture that there are $4[s^2]-2$ such arcs for $s \ge 1$, where $[x]$ denotes the integral part of $x$.Comment: 8 pages, latex, 3 uuencoded figure

Persistent current in superconducting nanorings

The superconductivity in very thin rings is suppressed by quantum phase slips. As a result the amplitude of the persistent current oscillations with flux becomes exponentially small, and their shape changes from sawtooth to a sinusoidal one. We reduce the problem of low-energy properties of a superconducting nanoring to that of a quantum particle in a sinusoidal potential and show that the dependence of the current on the flux belongs to a one-parameter family of functions obtained by solving the respective Schrodinger equation with twisted boundary conditions.Comment: 5 pages, 1 figur

The spin-incoherent Luttinger liquid

In contrast to the well known Fermi liquid theory of three dimensions, interacting one-dimensional and quasi one-dimensional systems of fermions are described at low energy by an effective theory known as Luttinger liquid theory. This theory is expressed in terms of collective many-body excitations that show exotic behavior such as spin-charge separation. Luttinger liquid theory is commonly applied on the premise that "low energy" describes both the spin and charge sectors. However, when the interactions in the system are very strong, as they typically are at low particle densities, the ratio of spin to charge energy may become exponentially small. It is then possible at very low temperatures for the energy to be low compared to the characteristic charge energy, but still high compared to the characteristic spin energy. This energy window of near ground-state charge degrees of freedom, but highly thermally excited spin degrees of freedom is called a spin-incoherent Luttinger liquid. The spin-incoherent Luttinger liquid exhibits a higher degree universality than the Luttinger liquid and its properties are qualitatively distinct. In this colloquium I detail some of the recent theoretical developments in the field and describe experimental indications of such a regime in gated semiconductor quantum wires.Comment: 21 pages, 18 figures. Updated references, corrected typo in Eq.(20) in journal versio

Gallot-Tanno Theorem for closed incomplete pseudo-Riemannian manifolds and applications

We extend the Gallot-Tanno Theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over a manifold admits a parallel symmetric $(0,2)-$tensor then it is Riemannian. Applications of this result to the existence of metrics with distinct Levi-Civita connections but having the same unparametrized geodesics and to the projective Obata conjecture are given. We also apply our result to show that the holonomy group of a closed $(O(p+1,q),S^{p,q})$-manifold does not preserve any nondegenerate splitting of $\R^{p+1,q}$.Comment: minor correction

Complex-Temperature Properties of the Ising Model on 2D Heteropolygonal Lattices

Using exact results, we determine the complex-temperature phase diagrams of the 2D Ising model on three regular heteropolygonal lattices, $(3 \cdot 6 \cdot 3 \cdot 6)$ (kagom\'{e}), $(3 \cdot 12^2)$, and $(4 \cdot 8^2)$ (bathroom tile), where the notation denotes the regular $n$-sided polygons adjacent to each vertex. We also work out the exact complex-temperature singularities of the spontaneous magnetisation. A comparison with the properties on the square, triangular, and hexagonal lattices is given. In particular, we find the first case where, even for isotropic spin-spin exchange couplings, the nontrivial non-analyticities of the free energy of the Ising model lie in a two-dimensional, rather than one-dimensional, algebraic variety in the $z=e^{-2K}$ plane.Comment: 31 pages, latex, postscript figure

The model of quality assessment of a scientific and educational network performance

The relevance of the studied problem is caused by the fact that now the creation need of transparent and objective models and mechanisms of educational quality assessment of the organizations with participation of professional communities, public organizations, and other interested parties is realized. The purpose of the publication consists in the model development of quality assessment of s scientific and educational network performance in the form of external audit. The system approach connected with representation, studying and designing of object as systems, sets of its interconnected structural and functional components, including in relation to research of the pedagogical phenomena and systems acts as the leading approach to research of this problem. The model of quality assessment of the scientific and educational network performance in the form of external audit is presented. Materials of the article can be useful while carrying out an independent assessment of current state and dynamics definition of the development of participants’ activity of network interaction (conditions, processes, results). © 2016 Tkacheva, Simonova & Matveev

Dramatic role of critical current anisotropy on flux avalanches in MgB2 films

Anisotropic penetration of magnetic flux in MgB2 films grown on vicinal sapphire substrates is investigated using magneto-optical imaging. Regular penetration above 10 K proceeds more easily along the substrate surface steps, anisotropy of the critical current being 6%. At lower temperatures the penetration occurs via abrupt dendritic avalanches that preferentially propagate {\em perpendicular} to the surface steps. This inverse anisotropy in the penetration pattern becomes dramatic very close to 10 K where all flux avalanches propagate in the strongest-pinning direction. The observed behavior is fully explained using a thermomagnetic model of the dendritic instability.Comment: 4 pages, 5 figure

Interaction effects in multi-subband quantum wires

We investigate the effect of electron-electron interactions on the transport properties of disordered quasi one-dimensional quantum wires with two or more subbands occupied. We apply two alternative methods to solve the logarithmic divergent problem, namely the parquet graph theory and a renormalization group calculation. We solve the group equations analytically in the weak coupling limit and find a power-law for the temperature dependent conductivity of a multi-channel system. The exponent is roughly equal to the inverse of the number of the occupied subbands.Comment: 4 pages, style-files included. No figure. Appears in J. Phys. Soc. Japan (Letter

Some New Results on Complex-Temperature Singularities in Potts Models on the Square Lattice

We report some new results on the complex-temperature (CT) singularities of $q$-state Potts models on the square lattice. We concentrate on the problematic region $Re(a) < 0$ (where $a=e^K$) in which CT zeros of the partition function are sensitive to finite lattice artifacts. From analyses of low-temperature series expansions for $3 \le q \le 8$, we establish the existence, in this region, of complex-conjugate CT singularities at which the magnetization and susceptibility diverge. From calculations of zeros of the partition function, we obtain evidence consistent with the inference that these singularities occur at endpoints $a_e, \ a_e^*$ of arcs protruding into the (complex-temperature extension of the) FM phase. Exponents for these singularities are determined; e.g., for $q=3$, we find $\beta_e=-0.125(1)$, consistent with $\beta_e=-1/8$. By duality, these results also imply associated arcs extending to the (CT extension of the) symmetric PM phase. Analytic expressions are suggested for the positions of some of these singularities; e.g., for $q=5$, our finding is consistent with the exact value $a_e,a_e^*=2(-1 \mp i)$. Further discussions of complex-temperature phase diagrams are given.Comment: 26 pages, latex, with eight epsf figure

Interaction Induced Restoration of Phase Coherence

We study the conductance of a quantum T-junction coupled to two electron reservoirs and a quantum dot. In the absence of electron-electron interactions, the conductance $g$ is sensitive to interference between trajectories which enter the dot and those which bypass it. We show that including an intra-dot charging interaction has a marked influence-- it can enforce a coherent response from the dot at temperatures much larger than the single particle level spacing $\Delta$. The result is large oscillations of $g$ as a function of the voltage applied to a gate capacitively coupled to the dot. Without interactions, the conductance has only a weak interference signature when $T>\Delta$.Comment: 4 pages, 2 figures. Typos corrected, minor changes for clarity. Accepted for publication in Phys. Rev. Let