The Hawking-Page phase transitions in the extended phase space in the Gauss-Bonnet gravity

In this paper, the Hawking-Page phase transitions between the black holes and thermal anti-de Sitter (AdS) space are studied with the Gauss-Bonnet term in the extended phase space, in which the varying cosmological constant plays the role of an effective thermodynamic pressure. The Gauss-Bonnet term exhibits its effects via introducing the corrections to the black hole entropy and Gibbs free energy. The global phase structures, especially the phase transition temperature $T_{\rm HP}$ and the Gibbs free energy $G$, are systematically investigated, first for the Schwarzschild-AdS black holes and then for the charged and rotating AdS black holes in the grand canonical ensembles, with both analytical and numerical methods. It is found that there are terminal points in the coexistence lines, and $T_{\rm HP}$ decreases at large electric potentials and angular velocities and also decreases with the Gauss-Bonnet coupling constant $\alpha$.Comment: 13 pages, 13 figure

A simple proof of exponential decay in the two dimensional percolation model

Kesten showed the exponential decay of percolation probability in the subcritical phase for the two-dimensional percolation model. This result implies his celebrated computation that $p_c=0.5$ for bond percolation in the square lattice, and site percolation in the triangular lattice, respectively. In this paper, we present a simpler proof for Kesten's theorem.Comment: 9 pages and one figur

Contribution of DKDK Continuum in the QCD Sum Rule for DsJ(2317)D_{sJ}(2317)

Using the soft-pion theorem and the assumption on the final-state interactions, we include the contribution of $DK$ continuum into the QCD sum rules for $D_{sJ}(2317)$ meson. We find that this contribution can significantly lower the mass and the decay constant of $D_s(0^+)$ state. For the value of the current quark mass $m_c(m_c)=1.286 {\rm GeV}$, we obtain the mass of $D_s(0^+)$ $M=2.33 \pm 0.02 {\rm GeV}$ in the interval $s_0=7.5-8.0 {\rm GeV}^2$, being in agreement with the experimental data, and the vector current decay constant of $D_s(0^+)$ $f_0=0.128 \pm 0.013 {\rm GeV}$, much lower than those obtained in previous literature

C2H N=1-0 and N2H+ J=1-0 observations of Planck Galactic cold clumps

A survey of C2H N=1-0 and N2H+ J=1-0 toward Planck Galactic cold clumps (PGCCs) was performed using the Purple Mountain Observatory's 13.7 m telescope. C2H and N2H+ were chosen to study the chemical evolutionary states of PGCCs. Among 121 observed molecular cores associated with PGCCs, 71 and 58 are detected with C2H N=1-0 and N2H+ J=1-0, respectively. The detected lines of most sources can be fitted with a single component with compatible Vlsr and line widths, which confirms that these PGCC cores are very cold (with gas temperatures 9-21 K) and quiescent while still dominanted by turbulence. The ratio between the column densities of C2H and N2H+ (N(C2H)/N(N2H+)) is found to be a good tracer for the evolutionary states of PGCC cores. Gas-grain chemical model can reproduce the decreasing trend of N(C2H)/N(N2H+) as a function of time. The cores with the lowest abundances of N2H+ (X[N2H+] < 10^{-10}) are the youngest, and have nearly constant abundances of C2H. In evolved cores with X[N2H+] ~ 1E-9, abundances of C2H drop quickly as the exhaustion of carbon atoms. Although these PGCC cores are in different evolutionary states, they are all quite young ( N(N2H+). Mapping observations are carried out toward 20 PGCC cores. The PGCC cores in Cepheus have lower N(C2H)/N(N2H+) and larger line widths compared with those in Taurus. This implies that PGCC cores in Taurus are less chemically evolved than those in Cepheus.Comment: 23 pages, 6 figures, 5 table