Abstract:
In Statistical Mechanics a standard assumption is that the description of the model under study doesn’t change whether we use canonical or microcanonical ensemble in the thermodynamic limit. This core assumption fails for certain systems. This phenomenon, called Breaking of Ensemble Equivalence (BEE), is known to happen for certain random network models and could be studied with the use of different equivalent approaches. Our goal is to find functions of the network (macrostates) whose asymptotic behavior shows detectable differences under the two different ensembles when BEE occurs. We will discuss how certain spectral properties of networks seem to be the right candidates in order to detect BEE.