Exact Finite-Size-Scaling Corrections to the Critical Two-Dimensional Ising Model on a Torus

We analyze the finite-size corrections to the energy and specific heat of the critical two-dimensional spin-1/2 Ising model on a torus. We extend the analysis of Ferdinand and Fisher to compute the correction of order L^{-3} to the energy and the corrections of order L^{-2} and L^{-3} to the specific heat. We also obtain general results on the form of the finite-size corrections to these quantities: only integer powers of L^{-1} occur, unmodified by logarithms (except of course for the leading $\log L$ term in the specific heat); and the energy expansion contains only odd powers of L^{-1}. In the specific-heat expansion any power of L^{-1} can appear, but the coefficients of the odd powers are proportional to the corresponding coefficients of the energy expansion.Comment: 26 pages (LaTeX). Self-unpacking file containing the tex file and three macros (indent.sty, eqsection.sty, subeqnarray.sty). Added discussions on the results and new references. Version to be published in J. Phys.

Kronecker's Double Series and Exact Asymptotic Expansion for Free Models of Statistical Mechanics on Torus

For the free models of statistical mechanics on torus, exact asymptotic expansions of the free energy, the internal energy and the specific heat in the vicinity of the critical point are found. It is shown that there is direct relation between the terms of the expansion and the Kronecker's double series. The latter can be expressed in terms of the elliptic theta-functions in all orders of the asymptotic expansion.Comment: REVTeX, 22 pages, this is expanded version which includes exact asymptotic expansions of the free energy, the internal energy and the specific hea

Bertotti-Robinson type solutions to Dilaton-Axion Gravity

We present a new solution to dilaton-axion gravity which looks like a rotating Bertotti-Robinson (BR) Universe. It is supported by an homogeneous Maxwell field and a linear axion and can be obtained as a near-horizon limit of extremal rotating dilaton-axion black holes. It has the isometry $SL(2,R)\times U(1)$ where U(1) is the remnant of the SO(3) symmetry of BR broken by rotation, while $SL(2,R)$ corresponds to the $AdS_2$ sector which no longer factors out of the full spacetime. Alternatively our solution can be obtained from the D=5 vacuum counterpart to the dyonic BR with equal electric and magnetic field strengths. The derivation amounts to smearing it in D=6 and then reducing to D=4 with dualization of one Kaluza-Klein two-form in D=5 to produce an axion. Using a similar dualization procedure, the rotating BR solution is uplifted to D=11 supergravity. We show that it breaks all supersymmetries of N=4 supergravity in D=4, and that its higher dimensional embeddings are not supersymmetric either. But, hopefully it may provide a new arena for corformal mechanics and holography. Applying a complex coordinate transformation we also derive a BR solution endowed with a NUT parameter.Comment: 21 page

Dynamic Critical Behavior of the Swendsen-Wang Algorithm: The Two-Dimensional 3-State Potts Model Revisited

We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen-Wang algorithm for the two-dimensional 3-state Potts model. We find that the Li-Sokal bound ($\tau_{int,E} \geq const \times C_H$) is almost but not quite sharp. The ratio $\tau_{int,E} / C_H$ seems to diverge either as a small power ($\approx 0.08$) or as a logarithm.Comment: 35 pages including 3 figures. Self-unpacking file containing the LaTeX file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and eqsection.sty) and the 3 Postscript figures. Revised version fixes a normalization error in \xi (with many thanks to Wolfhard Janke for finding the error!). To be published in J. Stat. Phys. 87, no. 1/2 (April 1997

Decomposing Dusty Galaxies. I. Multi-Component Spectral Energy Distribution Fitting

We present a new multi-component spectral energy distribution (SED) decomposition method and use it to analyze the ultraviolet to millimeter wavelength SEDs of a sample of dusty infrared-luminous galaxies. SEDs are constructed from spectroscopic and photometric data obtained with the Spitzer Space Telescope, in conjunction with photometry from the literature. Each SED is decomposed into emission from populations of stars, an AGN accretion disk, PAHs, atomic and molecular lines, and distributions of graphite and silicate grains. Decompositions of the SEDs of the template starburst galaxies NGC7714 and NGC2623 and the template AGNs PG0804+761 and Mrk463 provide baseline properties to aid in quantifying the strength of star-formation and accretion in the composite systems NGC6240 and Mrk1014. We find that obscured radiation from stars is capable of powering the total dust emission from NGC6240, although we cannot rule out a contribution from a deeply embedded AGN visible only in X-rays. The decomposition of Mrk1014 is consistent with ~65% of its power emerging from an AGN and ~35% from star-formation. We suggest that many of the variations in our template starburst SEDs may be explained in terms of the different mean optical depths through the clouds of dust surrounding the young stars within each galaxy. Prompted by the divergent far-IR properties of our template AGNs, we suggest that variations in the relative orientation of their AGN accretion disks with respect to the disks of the galaxies hosting them may result in different amounts of AGN-heated cold dust emission emerging from their host galaxies. We estimate that 30-50% of the far-IR and PAH emission from Mrk1014 may originate from such AGN-heated material in its host galaxy disk.Comment: 27 pages, 12 figures. Accepted for publication in the Ap

CASSIS: The Cornell Atlas of Spitzer/IRS Sources

We present the spectral atlas of sources observed in low resolution with the Infrared Spectrograph on board the Spitzer Space Telescope. More than 11,000 distinct sources were extracted using a dedicated algorithm based on the SMART software with an optimal extraction (AdOpt package). These correspond to all 13,000 low resolution observations of fixed objects (both single source and cluster observations). The pipeline includes image cleaning, individual exposure combination, and background subtraction. A particular attention is given to bad pixel and outlier rejection at the image and spectra levels. Most sources are spatially unresolved so that optimal extraction reaches the highest possible signal-to-noise ratio. For all sources, an alternative extraction is also provided that accounts for all of the source flux within the aperture. CASSIS provides publishable quality spectra through an online database together with several important diagnostics, such as the source spatial extent and a quantitative measure of detection level. Ancillary data such as available spectroscopic redshifts are also provided. The database interface will eventually provide various ways to interact with the spectra, such as on-the-fly measurements of spectral features or comparisons among spectra.Comment: Accepted for publication in ApJ Supplement Serie

CASSIS: The Cornell Atlas of Spitzer/Infrared Spectrograph Sources. II. High-resolution observations

The Infrared Spectrograph (IRS) on board the Spitzer Space Telescope observed about 15,000 objects during the cryogenic mission lifetime. Observations provided low-resolution (R~60-127) spectra over ~5-38um and high-resolution (R~600) spectra over ~10-37um. The Cornell Atlas of Spitzer/IRS Sources (CASSIS) was created to provide publishable quality spectra to the community. Low-resolution spectra have been available in CASSIS since 2011, and we present here the addition of the high-resolution spectra. The high-resolution observations represent approximately one third of all staring observations performed with the IRS instrument. While low-resolution observations are adapted to faint objects and/or broad spectral features (e.g., dust continuum, molecular bands), high-resolution observations allow more accurate measurements of narrow features (e.g., ionic emission lines) as well as a better sampling of the spectral profile of various features. Given the narrow aperture of the two high-resolution modules, cosmic ray hits and spurious features usually plague the spectra. Our pipeline is designed to minimize these effects through various improvements. A super sampled point-spread function was created in order to enable the optimal extraction in addition to the full aperture extraction. The pipeline selects the best extraction method based on the spatial extent of the object. For unresolved sources, the optimal extraction provides a significant improvement in signal-to-noise ratio over a full aperture extraction. We have developed several techniques for optimal extraction, including a differential method that eliminates low-level rogue pixels (even when no dedicated background observation was performed). The updated CASSIS repository now includes all the spectra ever taken by the IRS, with the exception of mapping observations

Worm algorithms for classical statistical models

We show that high-temperature expansions may serve as a basis for the novel approach to efficient Monte Carlo simulations. "Worm" algorithms utilize the idea of updating closed path configurations (produced by high-temperature expansions) through the motion of end points of a disconnected path. An amazing result is that local, Metropolis-type schemes may have dynamical critical exponents close to zero (i.e., their efficiency is comparable to the best cluster methods). We demonstrate this by calculating finite size scaling of the autocorrelation time for various (six) universality classes.Comment: 4 pages, latex, 2 figure

Irrelevant operators in the two-dimensional Ising model

By using conformal-field theory, we classify the possible irrelevant operators for the Ising model on the square and triangular lattices. We analyze the existing results for the free energy and its derivatives and for the correlation length, showing that they are in agreement with the conformal-field theory predictions. Moreover, these results imply that the nonlinear scaling field of the energy-momentum tensor vanishes at the critical point. Several other peculiar cancellations are explained in terms of a number of general conjectures. We show that all existing results on the square and triangular lattice are consistent with the assumption that only nonzero spin operators are present.Comment: 32 pages. Added comments and reference

PAH Emission from Ultraluminous Infrared Galaxies

We explore the relationships between the Polycyclic Aromatic Hydrocarbon (PAH) feature strengths, mid-infrared continuum luminosities, far-infrared spectral slopes, optical spectroscopic classifications, and silicate optical depths within a sample of 107 ULIRGs observed with the Infrared Spectrograph on the Spitzer Space Telescope. The detected 6.2 micron PAH equivalent widths (EQWs) in the sample span more than two orders of magnitude (0.006-0.8 micron), and ULIRGs with HII-like optical spectra or steep far-infrared spectral slopes (S_{25} / S_{60} < 0.2) typically have 6.2 micron PAH EQWs that are half that of lower-luminosity starbursts. A significant fraction (~40-60%) of HII-like, LINER-like, and cold ULIRGs have very weak PAH EQWs. Many of these ULIRGs also have large (tau_{9.7} > 2.3) silicate optical depths. The far-infrared spectral slope is strongly correlated with PAH EQW, but not with silicate optical depth. In addition, the PAH EQW decreases with increasing rest-frame 24 micron luminosity. We argue that this trend results primarily from dilution of the PAH EQW by continuum emission from dust heated by a compact central source, probably an AGN. High luminosity, high-redshift sources studied with Spitzer appear to have a much larger range in PAH EQW than seen in local ULIRGs, which is consistent with extremely luminous starburst systems being absent at low redshift, but present at early epochs.Comment: 15 pages, 9 Figures; Accepted for publication in Ap