Continuity of the Explosive Percolation Transition

The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is found to be well described by the power-law form with the decay exponent $\tau = 2.06(2)$, followed by a hump. We then use the finite-size scaling method to make all the distributions at various system sizes up to $N=2^{37}$ collapse perfectly onto a scaling curve characterized solely by the single exponent $\tau$. We also observe that the instant of that collapse converges to a well-defined percolation threshold from below as $N\rightarrow\infty$. Based on these observations, we show that the explosive percolation transition in the model should be continuous, contrary to the widely-spread belief of its discontinuity.Comment: Some corrections during the revie

Two-gap and paramagnetic pair-breaking effects on upper critical field of SmFeAsO0.85_{0.85} and SmFeAsO0.8_{0.8}F0.2_{0.2} single crystals

We investigated the temperature dependence of the upper critical field [$H_{c2}(T)$] of fluorine-free SmFeAsO$_{0.85}$ and fluorine-doped SmFeAsO$_{0.8}$F$_{0.2}$ single crystals by measuring the resistive transition in low static magnetic fields and in pulsed fields up to 60 T. Both crystals show that $H_{c2}(T)$'s along the c axis [$H_{c2}^c(T)$] and in an $ab$-planar direction [$H_{c2}^{ab}(T)$] exhibit a linear and a sublinear increase, respectively, with decreasing temperature below the superconducting transition. $H_{c2}(T)$'s in both directions deviate from the conventional one-gap Werthamer-Helfand-Hohenberg theoretical prediction at low temperatures. A two-gap nature and the paramagnetic pair-breaking effect are shown to be responsible for the temperature-dependent behavior of $H_{c2}^c$ and $H_{c2}^{ab}$, respectively.Comment: 21 pages, 8 figure

Neutron skin of 27^{27}Al with Skyrme and Korea-IBS-Daegu-SKKU density functionals

Recent measurement of the parity-violating (PV) asymmetry in the elastic electron scattering on $^{27}$Al target evokes the interest in the distribution of the neutron in the nucleus. In this work, we calculate the neutron skin thickness ($R_{np}$) of $^{27}$Al with nonrelativistic nuclear structure models. We focus on the role of the effective mass, symmetry energy and pairing force. Models are selected to have effective masses in the range $(0.58-1.05)M$ where $M$ is the nucleon mass in free space, and stiffness of the symmetry energy is varied by choosing the slope of the symmetry energy in the range 9.4 -- 100.5 MeV. Effect of pairing force is investigated by calculating $R_{np}$ with and without pairing, and using two different forms of the pairing force. With nine models, we obtain $R_{np} = 0.001 - 0.014$ fm. The result is independent of the effective mass, symmetry energy, and the form of pairing force. However, $R_{np}$ is negative when the pairing force is switched off, so the pairing force plays an essential role to make $R_{np}$ positive and constrained in a narrow range. We also calculate the PV asymmetry ($A_{\rm pv}$) in the elastic electron-$^{27}$Al scattering in the Born approximation at the kinematics of the Qweak experiment. We obtain a very narrow-ranged result $A_{\rm pv} =$ (2.07 -- 2.09) $\times 10^{-6}$. The result is consistent with the experiment and insensitive to the effective mass, symmetry energy and pairing force.Comment: 5 pages, 2 figure

Spectrum of Eleven-dimensional Supergravity on a PP-wave Background

We calculate the spectrum of the linearized supergravity around the maximally supersymmetric pp-wave background in eleven dimensions. The resulting spectrum agrees with that of zero-mode Hamiltonian of a supermembrane theory on the pp-wave background. We also discuss the connection with the Kaluza-Klein zero modes of AdS_4 x S^7 background.Comment: 17 pages, no figures, LaTeX2e, typos correcte

N=(4,4) Type IIA String Theory on PP-Wave Background

We construct IIA GS superstring action on the ten-dimensional pp-wave background, which arises as the compactification of eleven-dimensional pp-wave geometry along the isometry direction. The background geometry has 24 Killing spinors and among them, 16 components correspond to the non-linearly realized kinematical supersymmetry in the string action. The remaining eight components are linearly realized and shown to be independent of x^+ coordinate, which is identified with the world-sheet time coordinate of the string action in the light-cone gauge. The resultant dynamical N=(4,4) supersymmetry is investigated, which is shown to be consistent with the field contents of the action containing two free massive supermultiplets.Comment: latex, 15 pages; v2: typos corrected, polished, references adde