The critical temperature of the 2D-Ising model through Deep Learning Autoencoders

We investigate deep learning autoencoders for the unsupervised recognition of phase transitions in physical systems formulated on a lattice. We focus our investigation on the 2-dimensional ferromagnetic Ising model and then test the application of the autoencoder on the anti-ferromagnetic Ising model. We use spin configurations produced for the 2-dimensional ferromagnetic and anti-ferromagnetic Ising model in zero external magnetic field. For the ferromagnetic Ising model, we study numerically the relation between one latent variable extracted from the autoencoder to the critical temperature $T_c$. The proposed autoencoder reveals the two phases, one for which the spins are ordered and the other for which spins are disordered, reflecting the restoration of the $\mathbb{Z}_2$ symmetry as the temperature increases. We provide a finite volume analysis for a sequence of increasing lattice sizes. For the largest volume studied, the transition between the two phases occurs very close to the theoretically extracted critical temperature. We define as a quasi-order parameter the absolute average latent variable ${\tilde z}$, which enables us to predict the critical temperature. One can define a latent susceptibility and use it to quantify the value of the critical temperature $T_c(L)$ at different lattice sizes and that these values suffer from only small finite scaling effects. We demonstrate that $T_c(L)$ extrapolates to the known theoretical value as $L \to \infty$ suggesting that the autoencoder can also be used to extract the critical temperature of the phase transition to an adequate precision. Subsequently, we test the application of the autoencoder on the anti-ferromagnetic Ising model, demonstrating that the proposed network can detect the phase transition successfully in a similar way.Comment: 17 pages, 14 figures, accepted for publication in Eur. Phys. J.

PP-wave ππ\pi\pi scattering and the ρ\rho resonance from lattice QCD

We calculate the parameters describing elastic $I=1$, $P$-wave $\pi\pi$ scattering using lattice QCD with $2+1$ flavors of clover fermions. Our calculation is performed with a pion mass of $m_\pi \approx 320\:\:{\rm MeV}$ and a lattice size of $L\approx 3.6$ fm. We construct the two-point correlation matrices with both quark-antiquark and two-hadron interpolating fields using a combination of smeared forward, sequential and stochastic propagators. The spectra in all relevant irreducible representations for total momenta $|\vec{P}| \leq \sqrt{3} \frac{2\pi}{L}$ are extracted with two alternative methods: a variational analysis as well as multi-exponential matrix fits. We perform an analysis using L\"uscher's formalism for the energies below the inelastic thresholds, and investigate several phase shift models, including possible nonresonant contributions. We find that our data are well described by the minimal Breit-Wigner form, with no statistically significant nonresonant component. In determining the $\rho$ resonance mass and coupling we compare two different approaches: fitting the individually extracted phase shifts versus fitting the $t$-matrix model directly to the energy spectrum. We find that both methods give consistent results, and at a pion mass of $am_{\pi}=0.18295(36)_{stat}$ obtain $g_{\rho\pi\pi} = 5.69(13)_{stat}(16)_{sys}$, $am_\rho = 0.4609(16)_{stat}(14)_{sys}$, and $am_{\rho}/am_{N} = 0.7476(38)_{stat}(23)_{sys}$, where the first uncertainty is statistical and the second is the systematic uncertainty due to the choice of fit ranges.Comment: 20 pages, 12 figures, published versio

On Late Time Tails in an Extreme Reissner-Nordstr\"om Black Hole: Frequency Domain Analysis

In this brief note, we revisit the study of the leading order late time decay tails of massless scalar perturbations outside an extreme Reissner-Nordstr\"om black hole. Previous authors have analysed this problem in the time domain; we analyse the problem in the frequency domain. We first consider initial perturbations with generic regular behaviour across the horizon on characteristic surfaces. For this set-up, we reproduce some of the previous results of Sela [arXiv:1510.06169] using Fourier methods. Next, we consider related initial data on t=\mbox{const} hypersurfaces, and present decay results at timelike infinity, near future null infinity, and near the future horizon. Along the way, using the $r_* \to -r_*$ inversion symmetry of the extreme Reissner-Nordstr\"om spacetime, we relate the higher multipole Aretakis and Newman-Penrose constants for a massless scalar in this background.Comment: 22 pages; 2 figure

Retained Fractured Fragment of A Central Venous Catheter: A Minimally Invasive Approach to Safe Retrieval

BACKGROUND: Complication following fracture of a central venous catheter can be catastrophic to both the patient and the attending doctor. Catheter fracture has been attributed to several factors namely prolong mechanical force acting on the catheter, and forceful removal or insertion of the catheter.CASE DETAILS: In the present case, the fracture was suspected during the process of removal. The tip of the catheter was notably missing, and an emergency chest radiograph confirmed our diagnosis of a retained  fracture of central venous catheter. The retained portion was removed by the interventional radiologist using an endovascular loop snare and delivered through a femoral vein venotomy performed by the surgeon.CONCLUSION: Endovascular approach to retrieval of retained fractured catheters has helped tremendously to reduce associated morbidity and the need for major surgery. The role of surgery has become limited to  instances of failed endovascular retrieval and in remote geographical locations devoid of such specialty.KEYWORDS: Central venous catheter, fracture, endovascular, interventional radiolog

Towards the P-wave nucleon-pion scattering amplitude in the Δ(1232)\Delta (1232) channel

We use lattice QCD and the L\"uscher method to study elastic pion-nucleon scattering in the isospin $I = 3/2$ channel, which couples to the $\Delta(1232)$ resonance. Our $N_f=2+1$ flavor lattice setup features a pion mass of $m_\pi \approx 250$ MeV, such that the strong decay channel $\Delta \rightarrow \pi N$ is close to the threshold. We present our method for constructing the required lattice correlation functions from single- and two-hadron interpolating fields and their projection to irreducible representations of the relevant symmetry group of the lattice. We show preliminary results for the energy spectra in selected moving frames and irreducible representations, and extract the scattering phase shifts. Using a Breit-Wigner fit, we also determine the resonance mass $m_\Delta$ and the $g_{\Delta-\pi N}$ coupling.Comment: 14 pages, 7 figures, Proceedings of the 36th Annual International Symposium on Lattice Field Theory (Lattice 2018), 22-28 July 2018, Michigan State University, East Lansing, Michigan US