Evidence of exactness of the mean field theory in the nonextensive regime of long-range spin models

The q-state Potts model with long-range interactions that decay as 1/r^alpha subjected to an uniform magnetic field on d-dimensional lattices is analized for different values of q in the nonextensive regime (alpha between 0 and d). We also consider the two dimensional antiferromagnetic Ising model with the same type of interactions. The mean field solution and Monte Carlo calculations for the equations of state for these models are compared. We show that, using a derived scaling which properly describes the nonextensive thermodynamic behaviour, both types of calculations show an excellent agreement in all the cases here considered, except for alpha=d. These results allow us to extend to nonextensive magnetic models a previous conjecture which states that the mean field theory is exact for the Ising one.Comment: 10 pages, 4 figure

Constraints on the neutrino emission from the Galactic Ridge with the ANTARES telescope

A highly significant excess of high-energy astrophysical neutrinos has been reported by the IceCube Collaboration. Some features of the energy and declination distributions of IceCube events hint at a North/South asymmetry of the neutrino flux. This could be due to the presence of the bulk of our Galaxy in the Southern hemisphere. The ANTARES neutrino telescope, located in the Mediterranean Sea, has been taking data since 2007. It offers the best sensitivity to muon neutrinos produced by galactic cosmic ray interactions in this region of the sky. In this letter a search for an extended neutrino flux from the Galactic Ridge region is presented. Different models of neutrino production by cosmic ray propagation are tested. No excess of events is observed and upper limits for different neutrino flux spectral indices Gamma are set. For Gamma = 2.4 the 90% confidence level flux upper limit at 100 TeV for one neutrino flavour corresponds to phi(1f)(0) (100TeV) = 2.0 . 10(-17) GeV-1 cm(-2) s(-1) sr(-1). Under this assumption, at most two events of the IceCube cosmic candidates can originate from the Galactic Ridge. A simple power-law extrapolation of the Fermi-LAT flux to account for IceCube High Energy Starting Events is excluded at 90% confidence level. (C) 2016 The Authors. Published by Elsevier B.V