Categoria

Lezioni di dottorato

Data

2022-04-26 16:00 - 18:00

Luogo

Microsoft Teams

Affiliation

Dipartimento di Fisica ``E.R. Caianiello``

Area di Ricerca

2022-4-26 16:00:00

After this year Nobel prize in Physics to Giorgio Parisi I decided to prepare a short course on some of the arguments mostly touched by the prize motivations, namely disordered systems and complexity. These are the lecture notes of this course. Although the arguments are of a theoretical nature, I will also mention some experimental results the theory has to account for. The course is mostly addressed to Ph.D. students, but is thought as being self-contained, therefore there is no need of any previous knowledge of the matter, besides a sufficient mathematical back- ground; everything needed will be developed throughout the pro- gramme. For this reason, the course is addressed to Mathematics and Physics students (but also students coming from different scien- tific disciplines) as well as to researchers of various areas which are interested in such themes. In these notes I will briefly recall some basic concepts of Ther- modynamics and Statistical Mechanics, such as the statistical en- sembles, the phenomenon of phase transitions, spontaneous symme- try breaking, broken ergodicity, pure states, mean-field theories and universality. These concepts will be generalized to the realm of dis- ordered materials, particularly the frustrated ones, namely the class of spin-glass systems, particularly the (mean field) p-spin and the Sherrington-Kirkpatrick models. These models will be solved using the replica method. The replica symmetric solution will be worked out together with the solutions with different schemes of replica sym- metry breakings, up to the Parisi solution. I will also discuss some other models close to spin-glasses, like the random energy model and some complex optimization problems.

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