In this module the knowledge of statistical physics is developed, with a particular attention to modern aspects involving interacting systems and critical phenomena.

The student must acquire a deep knowledge and understanding of the statistical physics of interacting systems and of its methodologies, and must become able to solve models in this domain, using exact or approximate analytical approaches.

Mathematical analysis, general physics, quantum mechanics, probability theory.

1. Statistical physics Review: canonical and grand-canonical ensembles, non-interacting systems (10 hours). The Ising model: introduction and exact solutions in one dimension and on the fully connected graph (10 hours). Mean-field approximation (10 hours). Beyond mean-field approximation: Bethe-Peierls and belief propagation (5 hours). The two-dimensional Ising model: Peierls argument, low- and high-temperature expansions, free energy in zero field on a square lattice. The two-dimensional XY model at low temperatures (15 hours). An introduction to the real-space renormalization group (10 hours).

Frontal lectures, using mainly blackboard. Problems are proposed after completing each topic and then solved after a few lectures, so that students have time to try and find their own solutions.

M. Plischke and B. Bergersen, Equilibrium statistical physics, World scientific R.K. Pathria and P.D. Beale, Statistical mechanics, Academic Press L. Peliti, Statistical mechanics in a nutshell, Bollati Boringhieri J.P. Sethna, Entropy, order parameters and complexity, Clarendon Lecture notes and slides will be provided.

Dispense;

E' possibile sostenere l’esame in anticipo rispetto all’acquisizione della frequenza

Modalità di esame: Prova orale obbligatoria;

Exam: Compulsory oral exam;

... The exam is based on an oral test. The test typically involve questions on 2-3 topics, the first one being chosen by the student. The knowledge of statistical physics and its methodologies is tested by asking the student to derive proofs of the main results. The ability to solve models is tested by asking the student to compute partition functions or thermodynamical observables for models of interacting systems.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.