Comment on "Breakdown of the Internet under Intentional Attack"

We obtain the exact position of the percolation threshold in intentionally damaged scale-free networks.Comment: 1 page, to appear in Phys. Rev. Let

Stability of the Black Hole Horizon and the Landau Ghost

The stability of the black hole horizon is demanded by both cosmic censorship and the generalized second law of thermodynamics. We test the consistency of these principles by attempting to exceed the black hole extremality condition in various process in which a U(1) charge is added to a nearly extreme Reissner--Nordstr\"om black hole charged with a {\it different\/} type of U(1) charge. For an infalling spherical charged shell the attempt is foiled by the self--Coulomb repulsion of the shell. For an infalling classical charge it fails because the required classical charge radius exceeds the size of the black hole. For a quantum charge the horizon is saved because in order to avoid the Landau ghost, the effective coupling constant cannot be large enough to accomplish the removal.Comment: 12 pages, RevTe

Linear Response Calculations of Spin Fluctuations

A variational formulation of the time--dependent linear response based on the Sternheimer method is developed in order to make practical ab initio calculations of dynamical spin susceptibilities of solids. Using gradient density functional and a muffin-tin-orbital representation, the efficiency of the approach is demonstrated by applications to selected magnetic and strongly paramagnetic metals. The results are found to be consistent with experiment and are compared with previous theoretical calculations.Comment: 11 pages, RevTex; 3 Figures, postscript, high-resolution printing (~1200dpi) is desire

Chern-Simons matrix model: coherent states and relation to Laughlin wavefunctions

Using a coherent state representation we derive many-body probability distributions and wavefunctions for the Chern-Simons matrix model proposed by Polychronakos and compare them to the Laughlin ones. We analyze two different coherent state representations, corresponding to different choices for electron coordinate bases. In both cases we find that the resulting probability distributions do not quite agree with the Laughlin ones. There is agreement on the long distance behavior, but the short distance behavior is different.Comment: 15 pages, LaTeX; one reference added, abstract and section 5 expanded, typos correcte

Ising Model on Networks with an Arbitrary Distribution of Connections

We find the exact critical temperature $T_c$ of the nearest-neighbor ferromagnetic Ising model on an `equilibrium' random graph with an arbitrary degree distribution $P(k)$. We observe an anomalous behavior of the magnetization, magnetic susceptibility and specific heat, when $P(k)$ is fat-tailed, or, loosely speaking, when the fourth moment of the distribution diverges in infinite networks. When the second moment becomes divergent, $T_c$ approaches infinity, the phase transition is of infinite order, and size effect is anomalously strong.Comment: 5 page

Kondo model for the "0.7 anomaly" in transport through a quantum point contact

Experiments on quantum point contacts have highlighted an anomalous conductance plateau at $0.7 (2e^2/h)$, with features suggestive of the Kondo effect. Here we present an Anderson model for transport through a point contact which we analyze in the Kondo limit. Hybridization to the band increases abruptly with energy but decreases with valence, so that the background conductance and the Kondo temperature $T_K$ are dominated by different valence transitions. This accounts for the high residual conductance above $T_K$. A spin-polarized current is predicted for Zeeman splitting $g^* \mu_B B > k_B T_K,k_BT$.Comment: 4 page

Lattice Discretization in Quantum Scattering

The utility of lattice discretization technique is demonstrated for solving nonrelativistic quantum scattering problems and specially for the treatment of ultraviolet divergences in these problems with some potentials singular at the origin in two and three space dimensions. This shows that lattice discretization technique could be a useful tool for the numerical solution of scattering problems in general. The approach is illustrated in the case of the Dirac delta function potential.Comment: 9 page

Sandpile avalanche dynamics on scale-free networks

Avalanche dynamics is an indispensable feature of complex systems. Here we study the self-organized critical dynamics of avalanches on scale-free networks with degree exponent $\gamma$ through the Bak-Tang-Wiesenfeld (BTW) sandpile model. The threshold height of a node $i$ is set as $k_i^{1-\eta}$ with $0\leq\eta<1$, where $k_i$ is the degree of node $i$. Using the branching process approach, we obtain the avalanche size and the duration distribution of sand toppling, which follow power-laws with exponents $\tau$ and $\delta$, respectively. They are given as $\tau=(\gamma-2 \eta)/(\gamma-1-\eta)$ and $\delta=(\gamma-1-\eta)/(\gamma-2)$ for $\gamma<3-\eta$, 3/2 and 2 for $\gamma>3-\eta$, respectively. The power-law distributions are modified by a logarithmic correction at $\gamma=3-\eta$.Comment: 8 pages, elsart styl

On the Logarithmic Triviality of Scalar Quantum Electrodynamics

Using finite size scaling and histogram methods we obtain numerical results from lattice simulations indicating the logarithmic triviality of scalar quantum electrodynamics, even when the bare gauge coupling is chosen large. Simulations of the non-compact formulation of the lattice abelian Higgs model with fixed length scalar fields on $L^{4}$ lattices with $L$ ranging from $6$ through $20$ indicate a line of second order critical points. Fluctuation-induced first order transitions are ruled out. Runs of over ten million sweeps for each $L$ produce specific heat peaks which grow logarithmically with $L$ and whose critical couplings shift with $L$ picking out a correlation length exponent of $0.50(5)$ consistent with mean field theory. This behavior is qualitatively similar to that found in pure $\lambda\phi^{4}$.Comment: 9 page

Local moment formation in quantum point contacts

Spin-density-functional theory of quantum point contacts (QPCs) reveals the formation of a local moment with a net of one electron spin in the vicinity of the point contact - supporting the recent report of a Kondo effect in a QPC. The hybridization of the local moment to the leads decreases as the QPC becomes longer, while the onsite Coulomb-interaction energy remains almost constant.Comment: 10 pages, 3 figures, accepted for publication in Physical Review Letter