Soluble kagome Ising model in a magnetic field

An Ising model on the kagome lattice with super-exchange interactions is solved exactly under the presence of a nonzero external magnetic field. The model generalizes the super-exchange model introduced by Fisher in 1960 and is analyzed in light of a free-fermion model. We deduce the critical condition and present detailed analyses of its thermodynamic and magnetic properties. The system is found to exhibit a second-order transition with logarithmic singularities at criticality.Comment: 8 pages, 8 figures, references adde

Shakura-Sunyaev Disk Can Smoothly Match Advection-Dominated Accretion Flow

We use the standard Runge-Kutta method to solve the set of basic equations describing black hole accretion flows composed of two-temperature plasma. We do not invoke any extra energy transport mechanism such as thermal conduction and do not specify any ad hoc outer boundary condition for the advection-dominated accretion flow (ADAF) solution. We find that in the case of high viscosity and non-zero radiative cooling, the ADAF solution can have an asymptotic approach to the Shakura-Sunyaev disk (SSD) solution, and the SSD-ADAF transition radius is close to the central black hole. Our results further prove the mechanism of thermal instability-triggered SSD-ADAF transition suggested previously by Takeuchi & Mineshige and Gu & Lu.Comment: 10 pages, 2 figures, accepted for publication in ApJ Letter

Global Dynamics of Advection-Dominated Accretion Revisited

We numerically solve the set of dynamical equations describing advection-dominated accretion flows (ADAF) around black holes, using a method similar to that of Chakrabarti (1996a). We choose the sonic radius of the flow $R_s$ and the integration constant in angular momentum equation $j$ as free parameters, and integrate the equations from the sonic point inwards to see if the solution can extend supersonically to the black hole horizon, and outwards to see if and where an acceptable outer boundary of the flow can be found. We recover the ADAF-thin disk solution constructed in Narayan, Kato, & Honma (1997, NKH97), an representative paper of the previous works on global ADAF solutions, although in that paper an apparently very different procedure was adopted. We obtain a complete picture in the form of $R_s-j$ parameter space which sums up the situation of ADAF solution at a glance. For comparison we also present the distribution of global solutions for inviscid flows in the $R_s-j$ space, which supports the view that there should be some similarities between the dynamical behavior of ADAF and that of adiabatic flows, and that there should be a continuous change from the properties of viscous flows to those of inviscid ones.Comment: 24 pages with 15 figures, to appear in ApJ Vol. 52

Subgap states in dirty superconductors and their effect on dephasing in Josephson qubits

We present a theory of the subgap tails of the density of states in a diffusive superconductor containing magnetic impurities. We show that the subgap tails have two contributions: one arising from mesoscopic gap fluctuations, previously discussed by Lamacraft and Simons, and the other associated to the long-wave fluctuations of the concentration of magnetic impurities. We study the latter both in small superconducting grains and in bulk systems [$d=1,2,3$], and establish the dimensionless parameter that controls which of the two contributions dominates the subgap tails. We observe that these contributions are related to each other by dimensional reduction. We apply the theory to estimate the effects of a weak concentration of magnetic impurities [$\approx 1 {\rm p.p.m}$] on the phase coherence of Josephson qubits. We find that at these typical concentrations, magnetic impurities are relevant for the dephasing in large qubits, designed around a $10 {\rm \mu m}$ scale, where they limit the quality factor to be $Q<10^4-10^5$.Comment: 13 pages, 1 figur

Ising model on nonorientable surfaces: Exact solution for the Moebius strip and the Klein bottle

Closed-form expressions are obtained for the partition function of the Ising model on an M x N simple-quartic lattice embedded on a Moebius strip and a Klein bottle for finite M and N. The finite-size effects at criticality are analyzed and compared with those under cylindrical and toroidal boundary conditions. Our analysis confirms that the central charge is c=1/2.Comment: 8 pages, 3 eps figure

The (1+1)-dimensional Massive sine-Gordon Field Theory and the Gaussian Wave-functional Approach

The ground, one- and two-particle states of the (1+1)-dimensional massive sine-Gordon field theory are investigated within the framework of the Gaussian wave-functional approach. We demonstrate that for a certain region of the model-parameter space, the vacuum of the field system is asymmetrical. Furthermore, it is shown that two-particle bound state can exist upon the asymmetric vacuum for a part of the aforementioned region. Besides, for the bosonic equivalent to the massive Schwinger model, the masses of the one boson and two-boson bound states agree with the recent second-order results of a fermion-mass perturbation calculation when the fermion mass is small.Comment: Latex, 11 pages, 8 figures (EPS files

The Haldane Energy Gap of A Doped Linear-Chain Heisenberg Antiferromagnet

Using the valence-bond-solid (VBS) approach and the Schwinger boson mean field approximation, we study the dependence of the Haldane gap of a spin-1 linear chain Heisenberg antiferromagnet on impurity doping with different spins. The impurity spins affect the singlet pairing order parameter $\Delta$ and the constraint factor $\lambda$. As a result, the Haldane gap is reduced by a factor $\sim n_i^{2/3}$, with $n_i$ as the impurity concentration, and eventually collapses at $n_i \sim 1/\xi$ with $\xi$ as the VBS correlation length. This theoretical prediction can be verified by neutron scattering experiments.Comment: REVTEX, 12 pages, no figure

An accretion model for the growth of the central black hole associated with ionization instability in quasars

A possible accretion model associated with the ionization instability of quasar disks is proposed to address the growth of the central black hole harbored in the host galaxy.The mass ratio between black hole and its host galactic bulge is a nature consequence of our model.Comment: submitted to ApJ, 15 page