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    Scale Invariance in disordered systems: the example of the Random Field Ising Model

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    We show by numerical simulations that the correlation function of the random field Ising model (RFIM) in the critical region in three dimensions has very strong fluctuations and that in a finite volume the correlation length is not self-averaging. This is due to the formation of a bound state in the underlying field theory. We argue that this non perturbative phenomenon is not particular to the RFIM in 3-d. It is generic for disordered systems in two dimensions and may also happen in other three dimensional disordered systems

    Supernovae 2016bdu and 2005gl, and their link with SN 2009ip-like transients: another piece of the puzzle

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    Supernova (SN) 2016bdu is an unusual transient resembling SN 2009ip. SN 2009ip-like events are characterized by a long-lasting phase of erratic variability which ends with two luminous outbursts a few weeks apart. The second outburst is significantly more luminous (about 3 mag) than the first. In the case of SN 2016bdu, the first outburst (Event A) reached an absolute magnitude M(r) ~ -15.3 mag, while the second one (Event B) occurred over one month later and reached M(r) ~ -18 mag. By inspecting archival data, a faint source at the position of SN 2016bdu is detectable several times in the past few years. We interpret these detections as signatures of a phase of erratic variability, similar to that experienced by SN 2009ip between 2008 and mid-2012, and resembling the currently observed variability of the luminous blue variable SN 2000ch in NGC 3432. Spectroscopic monitoring of SN 2016bdu during the second peak initially shows features typical of a SN IIn. One month after the Event B maximum, the spectra develop broad Balmer lines with P Cygni profiles and broad metal features. At these late phases, the spectra resemble those of a typical Type II SN. All members of this SN 2009ip-like group are remarkably similar to the Type IIn SN 2005gl. For this object, the claim of a terminal SN explosion is supported by the disappearance of the progenitor star. The similarity with SN 2005gl suggests that all members of this family may finally explode as genuine SNe, although the unequivocal detection of nucleosynthesised elements in their nebular spectra is still missing.Comment: Submitted to MNRAS on April 10, 2017; re-submitted on June 23 including suggestions from the referee. 24 pages, 12 figures, 5 table

    SN 2009E: a faint clone of SN 1987A

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    In this paper we investigate the properties of SN 2009E, which exploded in a relatively nearby spiral galaxy (NGC 4141) and that is probably the faintest 1987A-like supernova discovered so far. Spectroscopic observations which started about 2 months after the supernova explosion, highlight significant differences between SN 2009E and the prototypical SN 1987A. Modelling the data of SN 2009E allows us to constrain the explosion parameters and the properties of the progenitor star, and compare the inferred estimates with those available for the similar SNe 1987A and 1998A. The light curve of SN 2009E is less luminous than that of SN 1987A and the other members of this class, and the maximum light curve peak is reached at a slightly later epoch than in SN 1987A. Late-time photometric observations suggest that SN 2009E ejected about 0.04 solar masses of 56Ni, which is the smallest 56Ni mass in our sample of 1987A-like events. Modelling the observations with a radiation hydrodynamics code, we infer for SN 2009E a kinetic plus thermal energy of about 0.6 foe, an initial radius of ~7 x 10^12 cm and an ejected mass of ~19 solar masses. The photospheric spectra show a number of narrow (v~1800 km/s) metal lines, with unusually strong Ba II lines. The nebular spectrum displays narrow emission lines of H, Na I, [Ca II] and [O I], with the [O I] feature being relatively strong compared to the [Ca II] doublet. The overall spectroscopic evolution is reminiscent of that of the faint 56Ni-poor type II-plateau supernovae. This suggests that SN 2009E belongs to the low-luminosity, low 56Ni mass, low-energy tail in the distribution of the 1987A-like objects in the same manner as SN 1997D and similar events represent the faint tail in the distribution of physical properties for normal type II-plateau supernovae.Comment: 19 pages, 9 figures (+7 in appendix); accepted for publication in A&A on 3 November 201
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