Phase transitions:introduction. Ising Model. Peierls result. Mean field theory. Rigourous results on thE Ising model. Renormalization group and spin blocks. Boltzmann equation. H theorem. Hydrodynamics.
The course is aimed at providing advanced preparation in the field of Statistical Mechanics of equilibrium and non-equilibrium, with knowledge of specialized topics of recent research in the field. The educational objectives include advanced knowledge of the physics of phase transitions and the Boltzmann equation and mathematical methods for their study. Ability to solve general problems in the field.
KNOWLEDGE AND UNDERSTANDING:
Students must have an in-depth understanding of the most important theories in the field of complex systems. They must also have a good knowledge of the state of the art in the field. The verification of knowledge and understanding is done through oral tests. The faculty is given to choose an untreated topic to be performed independently.
APPLYING KNOWLEDGE AND UNDERSTANDING:
Students must be able to identify the essential elements of a complex physical problem and know how to model them, making the necessary approximations.
They must be able to adapt existing models to new experimental data.
Students must be able to do calculations themselves or numerical simulations. Develop the ability to perform bibliographic searches and to select interesting materials, in particular on the WEB. Having achieved an adequate level of ethical awareness in research and in professional activities. These skills are acquired during the study for the preparation of the exams, deepening some specific topics also with the consultation of articles in journals.
Students must be able to work in groups. Being able to present their research or the results of a bibliographic search to an audience of both specialists and laymen.
Students must be able to tackle new fields through independent study. They must acquire the ability to continue their studies in a research doctorate or other graduate schools.