On free energies of the Ising model on the Cayley tree

We present, for the Ising model on the Cayley tree, some explicit formulae of the free energies (and entropies) according to boundary conditions (b.c.). They include translation-invariant, periodic, Dobrushin-like b.c., as well as those corresponding to (recently discovered) weakly periodic Gibbs states. The later are defined through a partition of the tree that induces a 4-edge-coloring. We compute the density of each color.Comment: 18 pages, 4 figure

The Pulse Scale Conjecture and the Case of BATSE Trigger 2193

The pulses that compose gamma-ray bursts (GRBs) are hypothesized to have the same shape at all energies, differing only by scale factors in time and amplitude. This "Pulse Scale Conjecture" is confirmed here between energy channels of the dominant pulse in GRB 930214c (BATSE trigger 2193), the single most fluent single-pulsed GRB that occurred before May 1998. Furthermore, pulses are hypothesized to start at the same time independent of energy. This "Pulse Start Conjecture" is also confirmed in GRB 930214c. Analysis of GRB 930214c also shows that, in general, higher energy channels show shorter temporal scale factors. Over the energy range 100 KeV - 1 MeV, it is found that the temporal scale factors between a pulse measured at different energies are related to that energy by a power law, possibly indicating a simple relativistic mechanism is at work. To test robustness, the Pulse Start and Pulse Scale Conjectures were also tested on the four next most fluent single-pulse GRBs. Three of the four clearly passed, with a second smaller pulse possibly confounding the discrepant test. Models where the pulse rise and decay are created by different phenomena do not typically predict pulses that satisfy both the Pulse Start Conjecture and the Pulse Scale Conjecture, unless both processes are seen to undergo common time dilation.Comment: 19 pages, 9 figures, analysis revised and extended, accepted to Ap

Feynman-Hellmann theorem for resonances and the quest for QCD exotica

The generalization of the Feynman-Hellmann theorem for resonance states in quantum field theory is derived. On the basis of this theorem, a criterion is proposed to study the possible exotic nature of certain hadronic states emerging in QCD. It is shown that this proposal is supported by explicit calculations in Chiral Perturbation Theory and by large-$N_c$ arguments. Analyzing recent lattice data on the quark mass dependence in the pseudoscalar, vector meson, baryon octet and baryon decuplet sectors, we conclude that, as expected, these are predominately quark-model states, albeit the corrections are non-negligible.Comment: 26 pages, 2 figure

Molecular Gas and Star Formation in the Cartwheel

Atacama Large Millimeter/submillimeter Array (ALMA) 12CO(J=1-0) observations are used to study the cold molecular ISM of the Cartwheel ring galaxy and its relation to HI and massive star formation (SF). CO moment maps find $(2.69\pm0.05)\times10^{9}$ M$_{\odot}$ of H$_2$ associated with the inner ring (72%) and nucleus (28%) for a Galactic I(CO)-to-N(H2) conversion factor ($\alpha_{\rm CO}$). The spokes and disk are not detected. Analysis of the inner ring's CO kinematics show it to be expanding ($V_{\rm exp}=68.9\pm4.9$ km s$^{-1}$) implying an $\approx70$ Myr age. Stack averaging reveals CO emission in the starburst outer ring for the first time, but only where HI surface density ($\Sigma_{\rm HI}$) is high, representing $M_{\rm H_2}=(7.5\pm0.8)\times10^{8}$ M$_{\odot}$ for a metallicity appropriate $\alpha_{\rm CO}$, giving small $\Sigma_{\rm H_2}$ ($3.7$ M$_{\odot}$ pc$^{-2}$), molecular fraction ($f_{\rm mol}=0.10$), and H$_2$ depletion timescales ($\tau_{\rm mol} \approx50-600$ Myr). Elsewhere in the outer ring $\Sigma_{\rm H_2}\lesssim 2$ M$_{\odot}$ pc$^{-2}$, $f_{\rm mol}\lesssim 0.1$ and $\tau_{\rm mol}\lesssim 140-540$ Myr (all $3\sigma$). The inner ring and nucleus are H$_2$-dominated and are consistent with local spiral SF laws. $\Sigma_{\rm SFR}$ in the outer ring appears independent of $\Sigma_{\rm H_2}$, $\Sigma_{\rm HI}$ or $\Sigma_{\rm HI+H_2}$. The ISM's long confinement in the robustly star forming rings of the Cartwheel and AM0644-741 may result in either a large diffuse H$_2$ component or an abundance of CO-faint low column density molecular clouds. The H$_2$ content of evolved starburst rings may therefore be substantially larger. Due to its lower $\Sigma_{\rm SFR}$ and age the Cartwheel's inner ring has yet to reach this state. Alternately, the outer ring may trigger efficient SF in an HI-dominated ISM.Comment: 10-pages text; 5-figure

Reconciling threshold and subthreshold expansions for pion-nucleon scattering

Heavy-baryon chiral perturbation theory (ChPT) at one loop fails in relating the pion-nucleon amplitude in the physical region and for subthreshold kinematics due to loop effects enhanced by large low-energy constants. Studying the chiral convergence of threshold and subthreshold parameters up to fourth order in the small-scale expansion, we address the question to what extent this tension can be mitigated by including the $\Delta(1232)$ as an explicit degree of freedom and/or using a covariant formulation of baryon ChPT. We find that the inclusion of the $\Delta$ indeed reduces the low-energy constants to more natural values and thereby improves consistency between threshold and subthreshold kinematics. In addition, even in the $\Delta$-less theory the resummation of $1/m_N$ corrections in the covariant scheme improves the results markedly over the heavy-baryon formulation, in line with previous observations in the single-baryon sector of ChPT that so far have evaded a profound theoretical explanation.Comment: 10 pages, 4 tables, Mathematica notebook with the analytic expressions for threshold and subthreshold parameters included as supplementary material; journal versio

On the Four-Dimensional Diluted Ising Model

In this letter we show strong numerical evidence that the four dimensional Diluted Ising Model for a large dilution is not described by the Mean Field exponents. These results suggest the existence of a new fixed point with non-gaussian exponents.Comment: 9 pages. compressed ps-file (uufiles

Critical properties of Ising model on Sierpinski fractals. A finite size scaling analysis approach

The present paper focuses on the order-disorder transition of an Ising model on a self-similar lattice. We present a detailed numerical study, based on the Monte Carlo method in conjunction with the finite size scaling method, of the critical properties of the Ising model on some two dimensional deterministic fractal lattices with different Hausdorff dimensions. Those with finite ramification order do not display ordered phases at any finite temperature, whereas the lattices with infinite connectivity show genuine critical behavior. In particular we considered two Sierpinski carpets constructed using different generators and characterized by Hausdorff dimensions d_H=log 8/log 3 = 1.8927.. and d_H=log 12/log 4 = 1.7924.., respectively. The data show in a clear way the existence of an order-disorder transition at finite temperature in both Sierpinski carpets. By performing several Monte Carlo simulations at different temperatures and on lattices of increasing size in conjunction with a finite size scaling analysis, we were able to determine numerically the critical exponents in each case and to provide an estimate of their errors. Finally we considered the hyperscaling relation and found indications that it holds, if one assumes that the relevant dimension in this case is the Hausdorff dimension of the lattice.Comment: 21 pages, 7 figures; a new section has been added with results for a second fractal; there are other minor change