Using zeros of the canonical partition function map to detect signatures of a Berezinskii-Kosterlitz-Thouless transition

Using the two dimensional $XY-(S(O(3))$ model as a test case, we show that analysis of the Fisher zeros of the canonical partition function can provide signatures of a transition in the Berezinskii-Kosterlitz-Thouless ($BKT$) universality class. Studying the internal border of zeros in the complex temperature plane, we found a scenario in complete agreement with theoretical expectations which allow one to uniquely classify a phase transition as in the $BKT$ class of universality. We obtain $T_{BKT}$ in excellent accordance with previous results. A careful analysis of the behavior of the zeros for both regions $\mathfrak{Re}(T) \leq T_{BKT}$ and $\mathfrak{Re}(T) > T_{BKT}$ in the thermodynamic limit show that $\mathfrak{Im}(T)$ goes to zero in the former case and is finite in the last one

A BGG-type resolution for tensor modules over general linear superalgebra

We construct a Bernstein-Gelfand-Gelfand type resolution in terms of direct sums of Kac modules for the finite-dimensional irreducible tensor representations of the general linear superalgebra. As a consequence it follows that the unique maximal submodule of a corresponding reducible Kac module is generated by its proper singular vector.Comment: 11pages, LaTeX forma

Eisenstein Series and String Thresholds

We investigate the relevance of Eisenstein series for representing certain $G(Z)$-invariant string theory amplitudes which receive corrections from BPS states only. $G(Z)$ may stand for any of the mapping class, T-duality and U-duality groups $Sl(d,Z)$, $SO(d,d,Z)$ or $E_{d+1(d+1)}(Z)$ respectively. Using $G(Z)$-invariant mass formulae, we construct invariant modular functions on the symmetric space $K\backslash G(R)$ of non-compact type, with $K$ the maximal compact subgroup of $G(R)$, that generalize the standard non-holomorphic Eisenstein series arising in harmonic analysis on the fundamental domain of the Poincar\'e upper half-plane. Comparing the asymptotics and eigenvalues of the Eisenstein series under second order differential operators with quantities arising in one- and $g$-loop string amplitudes, we obtain a manifestly T-duality invariant representation of the latter, conjecture their non-perturbative U-duality invariant extension, and analyze the resulting non-perturbative effects. This includes the $R^4$ and $R^4 H^{4g-4}$ couplings in toroidal compactifications of M-theory to any dimension $D\geq 4$ and $D\geq 6$ respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms renumbered, plus minor corrections; v3: relation (1.7) to math Eis series clarified, eq (3.3) and minor typos corrected, final version to appear in Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde

HST Survey of Clusters in Nearby Galaxies. II. Statistical Analysis of Cluster Populations

We present a statistical system that can be used in the study of cluster populations. The basis of our approach is the construction of synthetic cluster color-magnitude-radius diagrams (CMRDs), which we compare with the observed data using a maximum likelihood calculation. This approach permits a relatively easy incorporation of incompleteness (a function of not only magnitude and color, but also radius), photometry errors and biases, and a variety of other complex effects into the calculation, instead of the more common procedure of attempting to correct for those effects. We then apply this procedure to our NGC 3627 data from Paper I. We find that we are able to successfully model the observed CMRD and constrain a number of parameters of the cluster population. We measure a power law mass function slope of alpha = -1.50 +/- 0.07, and a distribution of core radii centered at r_c = 1.53 +/- 0.15 pc. Although the extinction distribution is less constrained, we measured a value for the mean extinction consistent with that determined in Paper I from the Cepheids.Comment: 21 pages, 3 figures accepted for publication by A

Tuning the electrical conductivity of nanotube-encapsulated metallocene wires

We analyze a new family of carbon nanotube-based molecular wires, formed by encapsulating metallocene molecules inside the nanotubes. Our simulations, that are based on a combination of non-equilibrium Green function techniques and density functional theory, indicate that these wires can be engineered to exhibit desirable magnetotransport effects for use in spintronics devices. The proposed structures should also be resilient to room-temperature fluctuations, and are expected to have a high yield.Comment: 4 pages, 6 figures. Accepted in Physical Review Letter

Electromagnetic Fields of Slowly Rotating Magnetized Gravastars

We study the dipolar magnetic field configuration and present solutions of Maxwell equations in the internal background spacetime of a a slowly rotating gravastar. The shell of gravastar where magnetic field penetrated is modeled as sphere consisting of perfect highly magnetized fluid with infinite conductivity. Dipolar magnetic field of the gravastar is produced by a circular current loop symmetrically placed at radius $a$ at the equatorial plane.Comment: 5 pages, 2 figures, accepted for publication to Mod. Phys. Lett.