Ensemble inequivalence in mean-field models
Stefano Ruffo


Abstract
I will discuss the problem of ``ensemble inequivalence": the disagreement in the value of averages (energy, temperature, etc.)in different statistical ensembles which persists in the thermodynamic limit. This can appear when the interaction is long-range, i.e. potentials decay at large distances with a power less or equal than the Euclidean space dimension. A large class of long-range interactions that is frequently introduced in statistical physics is the one of mean-field models. We have been able to solve exactly some mean-field models (e.g. the Blume-Emery-Griffiths model), both in the canonical and in the microcanonical ensemble and to prove that these give inequivalent predictions when the system is inhomogeneous, for instance at a first-order phase transition. In particular, we have shown that negative specific heat and temperature jumps (the equivalent of energy jumps, so-called latent heat, in the canonical ensemble) can arise in the microcanonical ensemble. We have moreover displayed a formal connection between such behaviours and a mean-field like structure of the partition function, allowing us to guess that all models of the mean-field type are expected to display ensemble inequivalence as well as the peculiar behaviour described above in the microcanonical ensemble.

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Elenco dei partecipanti al convegno di Bari.

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