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Center for Nonlinear Studies |
In recent years the idea of statistical ensemble inequivalence has drawn considerable interest, in part due to the experimental and theoretical observation of phenomena of negative specific heat. First observed in self-gravitating systems like galaxies or solar systems, ensemble inequivalence was first thought to be present only in systems with long range interactions, but recent developments indicate that it is also a consequence of a large surface to bulk energy ratio (as in some nuclear and molecular systems) and with other types of non-additive systems. We will study in some detail ferromagnetic spin systems in different types of networks and graphs such as K-regular, Erdos-Rnyi and small world networks. The motivation for this study is the fact that due to their structure, these types of networks are intrinsically non-additive. We will perform canonical and micro-canonical calculations using combinatorial approaches, numerical simulations and the cavity method and will consider both annealed and quenched disorder.