Phase Transitions in Disordered Systems: The Example of the Random-Field Ising Model in Four Dimensions

By performing a high-statistics simulation of the D = 4 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to describe the transition.

Space density distribution of galaxies in the absolute magnitude - rotation velocity plane: a volume-complete Tully-Fisher relation from CALIFA stellar kinematics

We measured the distribution in absolute magnitude - circular velocity space for a well-defined sample of 199 rotating galaxies of the Calar Alto Legacy Integral Field Area Survey (CALIFA) using their stellar kinematics. Our aim in this analysis is to avoid subjective selection criteria and to take volume and large-scale structure factors into account. Using stellar velocity fields instead of gas emission line kinematics allows including rapidly rotating early-type galaxies. Our initial sample contains 277 galaxies with available stellar velocity fields and growth curve r-band photometry. After rejecting 51 velocity fields that could not be modelled because of the low number of bins, foreground contamination, or significant interaction, we performed Markov chain Monte Carlo modelling of the velocity fields, from which we obtained the rotation curve and kinematic parameters and their realistic uncertainties. We performed an extinction correction and calculated the circular velocity v_circ accounting for the pressure support of a given galaxy. The resulting galaxy distribution on the M-r - v(circ) plane was then modelled as a mixture of two distinct populations, allowing robust and reproducible rejection of outliers, a significant fraction of which are slow rotators. The selection effects are understood well enough that we were able to correct for the incompleteness of the sample. The 199 galaxies were weighted by volume and large-scale structure factors, which enabled us to fit a volume-corrected Tully-Fisher relation (TFR). More importantly, we also provide the volume-corrected distribution of galaxies in the M_r - v_circ plane, which can be compared with cosmological simulations. The joint distribution of the luminosity and circular velocity space densities, representative over the range of -20 > M_r > -22 mag, can place more stringent constraints on the galaxy formation and evolution scenarios than linear TFR fit parameters or the luminosity function alone.

The effect of the geomagnetic field on cosmic ray energy estimates and large scale anisotropy searches on data from the Pierre Auger Observatory

We present a comprehensive study of the influence of the geomagnetic field on the energy estimation of extensive air showers with a zenith angle smaller than 60 degrees, detected at the Pierre Auger Observatory. the geomagnetic field induces an azimuthal modulation of the estimated energy of cosmic rays up to the similar to 2% level at large zenith angles. We present a method to account for this modulation of the reconstructed energy. We analyse the effect of the modulation on large scale anisotropy searches in the arrival direction distributions of cosmic rays. At a given energy, the geomagnetic effect is shown to induce a pseudo-dipolar pattern at the percent level in the declination distribution that needs to be accounted for.

Deep observation of the NGC1275 region with MAGIC: search of diffuse gamma-ray emission from cosmic rays in the Perseus cluster

Clusters of galaxies are expected to be reservoirs of cosmic rays (CRs) that should produce diffuse γ-ray emission due to their hadronic interactions with the intra-cluster medium. The nearby Perseus cool-core cluster, identified as the most promising target to search for such an emission, has been observed with the MAGIC telescopes at very-high energies (VHE, E ≥ 100 GeV) for a total of 253 hr from 2009 to 2014. The active nuclei of NGC 1275, the central dominant galaxy of the cluster, and IC 310, lying at about 0.6º from the centre, have been detected as point-like VHE γ-ray emitters during the first phase of this campaign. We report an updated measurement of the NGC 1275 spectrum, which is described well by a power law with a photon index Γ = 3.6 ± 0.2_(stat) ± 0.2_(syst) between 90 GeV and 1200 GeV. We do not detect any diffuse γ-ray emission from the cluster and so set stringent constraints on its CR population. To bracket the uncertainties over the CR spatial and spectral distributions, we adopt different spatial templates and power-law spectral indexes α. For α = 2.2, the CR-to-thermal pressure within the cluster virial radius is constrained to be ≤ 1 − 2%, except if CRs can propagate out of the cluster core, generating a flatter radial distribution and releasing the CR-to-thermal pressure constraint to ≤ 20%. Assuming that the observed radio mini-halo of Perseus is generated by secondary electrons from CR hadronic interactions, we can derive lower limits on the central magnetic field, B_(0), that depend on the CR distribution. For α = 2.2, B_(0) ≥ 5 − 8 µG, which is below the ∼25 µG inferred from Faraday rotation measurements, whereas for α ≤ 2.1, the hadronic interpretation of the diffuse radio emission contrasts with our γ-ray flux upper limits independently of the magnetic field strength.