Scaling law of Wolff cluster surface energy

We study the scaling properties of the clusters grown by the Wolff algorithm on seven different Sierpinski-type fractals of Hausdorff dimension $1 < d_f \le 3$ in the framework of the Ising model. The mean absolute value of the surface energy of Wolff cluster follows a power law with respect to the lattice size. Moreover, we investigate the probability density distribution of the surface energy of Wolff cluster and are able to establish a new scaling relation. It enables us to introduce a new exponent associated to the surface energy of Wolff cluster. Finally, this new exponent is linked to a dynamical exponent via an inequality.Comment: 12 pages, 3 figures. To appear in PR

Explicit Space-Time Codes Achieving The Diversity-Multiplexing Gain Tradeoff

A recent result of Zheng and Tse states that over a quasi-static channel, there exists a fundamental tradeoff, referred to as the diversity-multiplexing gain (D-MG) tradeoff, between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space-time (ST) block code. This tradeoff is precisely known in the case of i.i.d. Rayleigh-fading, for T>= n_t+n_r-1 where T is the number of time slots over which coding takes place and n_t,n_r are the number of transmit and receive antennas respectively. For T < n_t+n_r-1, only upper and lower bounds on the D-MG tradeoff are available. In this paper, we present a complete solution to the problem of explicitly constructing D-MG optimal ST codes, i.e., codes that achieve the D-MG tradeoff for any number of receive antennas. We do this by showing that for the square minimum-delay case when T=n_t=n, cyclic-division-algebra (CDA) based ST codes having the non-vanishing determinant property are D-MG optimal. While constructions of such codes were previously known for restricted values of n, we provide here a construction for such codes that is valid for all n. For the rectangular, T > n_t case, we present two general techniques for building D-MG-optimal rectangular ST codes from their square counterparts. A byproduct of our results establishes that the D-MG tradeoff for all T>= n_t is the same as that previously known to hold for T >= n_t + n_r -1.Comment: Revised submission to IEEE Transactions on Information Theor

The Origin of C IV Absorption Systems at Redshifts z<1---Discovery of Extended C IV Envelopes Around Galaxies

(Abridged) We report the discovery of extended CIV gaseous envelopes around galaxies of a wide range of luminosity and morphological type. First, we show that CIV absorption systems are strongly clustered around galaxies on velocity scales of v < 250 km/s and impact parameter scales of rho < 100 h^{-1} kpc but not on larger velocity or impact parameter scales. Next, adopting measurements of galaxy properties presented in previous papers, we examine how properties of the CIV absorption systems depend on properties of the galaxies. On the basis of 14 galaxy and absorber pairs and 36 galaxies that do not produce corresponding CIV absorption lines to within sensitive upper limits, we find that: (1) Galaxies of a range of morphological type and luminosity appear to possess extended CIV gaseous envelopes of radius R ~ 100 h^{-1} kpc, with abrupt boundaries between the CIV absorbing and non-absorbing regions. (2) The extent of CIV-absorbing gas around galaxies scales with galaxy B-band luminosity as R \propto L_B^{0.5 +/- 0.1} but does not depend strongly on galaxy surface brightness, redshift, or morphological type. And (3) the covering factor of CIV clouds within ~ 100 h^{-1} kpc of galaxies is nearly unity, but there is a large scatter in the mean number of clouds encountered along the line of sight. The most significant implication of the study is that galaxies of a wide range of luminosity and morphological type are surrounded by chemically enriched gas that extends for at least ~ 100 h^{-1} kpc. We consider various scenarios that may have produced metals at large galactic distance and conclude that accreting satellites are most likely to be responsible for chemically enriched gas at large galactic distances to regular looking galaxies.Comment: 19 pages, 3 figures, to appear in ApJ, July 20 200

Near-IR studies of recurrent nova V745 Scorpii during its 2014 outburst

The recurrent nova (RN) V745 Scorpii underwent its third known outburst on 2014 February 6. Infrared monitoring of the eruption on an almost daily basis, starting from 1.3d after discovery, shows the emergence of a powerful blast wave generated by the high velocity nova ejecta exceeding 4000 kms$^{-1}$ plowing into its surrounding environment. The temperature of the shocked gas is raised to a high value exceeding 10$^{8}$K immediately after outburst commencement. The energetics of the outburst clearly surpass those of similar symbiotic systems like RS Oph and V407 Cyg which have giant secondaries. The shock does not show a free-expansion stage but rather shows a decelerative Sedov-Taylor phase from the beginning. Such strong shockfronts are known to be sites for $\gamma$ ray generation. V745 Sco is the latest nova, apart from five other known novae, to show $\gamma$ ray emission. It may be an important testbed to resolve the crucial question whether all novae are generically $\gamma$ ray emitters by virtue of having a circumbinary reservoir of material that is shocked by the ejecta rather than $\gamma$ ray generation being restricted to only symbiotic systems with a shocked red giant (RG) wind. The lack of a free-expansion stage favors V745 Sco to have a density enhancement around the white dwarf (WD), above that contributed by a RG wind. Our analysis also suggests that the WD in V745 Sco is very massive and a potential progenitor for a future SN Ia explosion.Comment: To appear in ApJ (Letters

Critical Behavior of the Ferromagnetic Ising Model on a Sierpinski Carpet: Monte Carlo Renormalization Group Study

We perform a Monte Carlo Renormalization Group analysis of the critical behavior of the ferromagnetic Ising model on a Sierpi\'nski fractal with Hausdorff dimension $d_f\simeq 1.8928$. This method is shown to be relevant to the calculation of the critical temperature $T_c$ and the magnetic eigen-exponent $y_h$ on such structures. On the other hand, scaling corrections hinder the calculation of the temperature eigen-exponent $y_t$. At last, the results are shown to be consistent with a finite size scaling analysis.Comment: 16 pages, 7 figure

Critical behavior of the 3-state Potts model on Sierpinski carpet

We study the critical behavior of the 3-state Potts model, where the spins are located at the centers of the occupied squares of the deterministic Sierpinski carpet. A finite-size scaling analysis is performed from Monte Carlo simulations, for a Hausdorff dimension $d_{f}$ $\simeq 1.8928$. The phase transition is shown to be a second order one. The maxima of the susceptibility of the order parameter follow a power law in a very reliable way, which enables us to calculate the ratio of the exponents $\gamma /\nu$. We find that the scaling corrections affect the behavior of most of the thermodynamical quantities. However, the sequence of intersection points extracted from the Binder's cumulant provides bounds for the critical temperature. We are able to give the bounds for the exponent $1/\nu$ as well as for the ratio of the exponents $\beta/\nu$, which are compatible with the results calculated from the hyperscaling relation.Comment: 13 pages, 4 figure

Coherent-State Approach to Two-dimensional Electron Magnetism

We study in this paper the possible occurrence of orbital magnetim for two-dimensional electrons confined by a harmonic potential in various regimes of temperature and magnetic field. Standard coherent state families are used for calculating symbols of various involved observables like thermodynamical potential, magnetic moment, or spatialdistribution of current. Their expressions are given in a closed form and the resulting Berezin-Lieb inequalities provide a straightforward way to study magnetism in various limit regimes. In particular, we predict a paramagnetic behaviour in the thermodynamical limit as well as in the quasiclassical limit under a weak field. Eventually, we obtain an exact expression for the magnetic moment which yields a full description of the phase diagram of the magnetization.Comment: 21 pages, 6 figures, submitted to PR

Abundance Profiles and Kinematics of Damped Lyman-alpha Absorbing Galaxies at z < 0.65

We present a spectroscopic study of six damped Lya absorption (DLA) systems at z<0.65, based on moderate-to-high resolution spectra of the galaxies responsible for the absorbers. Combining known metallicity measurements of the absorbers with known optical properties of the absorbing galaxies, we confirm that the low metal content of the DLA population can arise naturally as a combination of gas cross-section selection and metallicity gradients commonly observed in local disk galaxies. We also study the Tully-Fisher relation of the DLA-selected galaxies and find little detectable evidence for evolution in the disk population between z=0 and z~0.5. Additional results of our analysis are as follows. (1) The DLA galaxies exhibit a range of spectral properties, from post-starburst, to normal disks, and to starburst systems, supporting the idea that DLA galaxies are drawn from the typical field population. (2) Large rotating HI disks of radius 30 h^{-1} kpc and of dynamic mass M_dyn > 10^{11} h^{-1} M_sun appear to be common at intermediate redshifts. (3) Using an ensemble of six galaxy-DLA pairs, we derive an abundance profile that is characterized by a radial gradient of -0.041 +/- 0.012 dex per kiloparsec (or equivalently a scale length of 10.6 h^{-1} kpc) from galactic center to 30 h^{-1} kpc radius. (4) Adopting known N(HI) profiles of nearby galaxies and the best-fit radial gradient, we further derive an N(HI)-weighted mean metallicity _weighted = -0.50 +/- 0.07 for the DLA population over 100 random lines of sight, consistent with _weighted = -0.64 (-0.86, +0.40) observed for z~1 DLA systems from Prochaska et al. Our analysis demonstrates that the low metal content of DLA systems does not rule out the possibility that the DLA population trace the field galaxy population.Comment: 57 pages, 17 figures, to appear in the ApJ 20 February 2005 issue; a pdf version of the paper with full-resolution figures is available at http://falcon.mit.edu/~hchen/public/tmp/dlachem.pd