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Theq-state gauge Potts modelPq ind-dimensions has been studied using Monte Carlo techniques. Ford=2 no phase transitions were detected. TheP2 model ford=3 shows a second order phase transition. On the other hand, all thed=3 (q?2) andd=4 cases studied show first order phase transitions. In these cases, it was possible to estimate transition coupling parameters as well as latent heat. For selected cases, a study of the behavior of the Wilson loop factor was done.

The results of high energy simulated experiments where a given hadronic particle impacts on a given target are statistically analyzed. The energy range of the projectiles goes from below the LHC scale up to the highest cosmic ray energies. This study was carried out by using the pre- and post-LHC versions of the hadronic interaction models QGSJET, EPOS and SIBYLL. Our analysis indicates that the post-LHC models present smaller differences in various quantities that characterize the secondary particles produced after the hadronic collisions, in comparison with the corresponding differences that are found comparing the respective old (pre-LHC) versions of the hadronic models. However, it is also found that there exist some discrepancies among models that persist even at the LHC energy scale, that call for further theoretical investigation. An additional analysis of the impact that different modeling of hadronic collisions has on air shower development is also included. It consists of a detailed study of the impact of the different pre- and post-LHC versions of the hadronic models considered, for relevant observables like the muon production depth distribution. [ABSTRACT FROM AUTHOR]