The purpose is to illustrate the theoretical approach to the analysis of critical phenomena through the renormalization group theory in real space. We will also introduce numerical algorithms for the analysis of critical properties. We expect an in- depth understanding of this topics. Ising model.

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Information on the course unit. ECTS: details. Course unit organization. Prerequisites: Statistical Mechanics course given at the third year of the laurea triennale Thermodynamics Target skills and knowledge: After completing the course the student should be able to understand and explain the basic concepts and the use of advanced techniques in statistical mechanics.

In particular the student should 1 give an account of the relevant quantities used to describe macroscopic systems, thermodynamic potentials and ensemble.

In this way we should be able to test the knowledge, the scientific vocabulary, the ability to synthesis and critical discussion acquired during the course. The second part of the exam will be oral and will be based on a discussion on the various topics discussed in class.

Assessment criteria: The criteria used to verify the knowledge and skills acquired are: 1 understanding of the topics covered; 2 critical ability to connect the acquired knowledge; 3 completeness of the acquired knowledge; 4 synthesis ability; 5 understanding of the terminology used 6 ability to use the analytical methodologies and techniques illustrated during the course to solve or at least set problems where statistical mechanics plays an important role.

Course unit contents: In short the contents of the program can be summarised as follows: Thermodynamics of phase transitions. Critical points, order parameters and critical exponents. Phase transitions and spontaneous symmetry breaking. Analytical tools to solve spins model in 1D, transfer matrix formalisms. Mean field theories. Ginzburg Landau theory.

Ginzburg criterium and upper critical dimension. Scaling theory and Kadanoff block spin argument. Renormalisation group in real space. Please note that some topics may vary Spontaneous symmetry breaking for continuous symmetry. Goldstone's theorem.

Planned learning activities and teaching methods: The course is organized in lectures whose contents are presented on the blackboard, sometimes with the help of images, diagrams and videos.

The teaching is interactive, with questions and presentation of case studies, forpromote discussion and critical reflection in the classroom. Huang, Meccanica Statistica. Peliti, Statistical Mechanics in a Nutshell. Yeomans, Statistical mechanics of Phase transitions.

Oxford: Oxford University Press, Innovative teaching methods: Teaching and learning strategies. Lecturing Questioning Problem solving Loading of files and pages web pages, Moodle, Innovative teaching methods: Software or applications used. Moodle files, quizzes, workshops, First cycle degree courses. Second cycle degree courses. Single cycle degree courses. Department of Physics and Astronomy. Statistical Mechanics course given at the third year of the laurea triennale Thermodynamics.

After completing the course the student should be able to understand and explain the basic concepts and the use of advanced techniques in statistical mechanics.

The verification of the acquired knowledge takes place through a common written test with exercises to be solved analytically and open questions on basic concepts.

The criteria used to verify the knowledge and skills acquired are: 1 understanding of the topics covered; 2 critical ability to connect the acquired knowledge; 3 completeness of the acquired knowledge; 4 synthesis ability; 5 understanding of the terminology used 6 ability to use the analytical methodologies and techniques illustrated during the course to solve or at least set problems where statistical mechanics plays an important role.

In short the contents of the program can be summarised as follows: Thermodynamics of phase transitions. Planned learning activities and teaching methods:. The course is organized in lectures whose contents are presented on the blackboard, sometimes with the help of images, diagrams and videos. Textbooks and optional supplementary readings.

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## 31552 - Statistical Mechanics 1

We'd like to understand how you use our websites in order to improve them. Register your interest. An effective Microcanonical Thermodynamics of self gravitating systems SGS is proposed, analyzing the well known obstacles thought to prevent the formulation of a rigorous Statistical Mechanics SM , as those due to the formal unboundedness of available phase space and to the unscreened, long range, nature of the interaction. The latter feature entails the well known in equivalence of statistical ensembles, puts clearly into question the meaning, for these systems, of the Thermodynamic Limit , and rules out the use of canonical and grand-canonical ensembles. As to the first obstacle , we argue nevertheless that a hierarchy of timescales exist such that, at any finite time , the volume of the effectively available region of phase space is indeed finite, and that the dynamics satisfies a strong chaos criterion, leading to a fast , increasingly uniform, spreading of orbits over an effectively invariant subset of the constant N,V,E surface; thus leading to the definition of a secularly evolving, generalized microcanonical ensemble , which allows to define an almost extensive effective entropy and to derive self-consistent definitions for other thermodynamic variables, giving thus an orthode for SGS. Moreover, a Second Law-like criterion allows to single out the hierarchy of secular equilibria describing, for any finite time, the macroscopic behaviour of SGS.

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## MECCANICA STATISTICA II

Search this site. Roberto Raimondi. Conferences and Events. PhD students. Useful links. Looking for a PhD in Physics? Teorema di fluttuazione-dissipazione.

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## Meccanica Statistica Elementare : I Fondamenti

Teacher Elisa Ercolessi. Credits 6. Teaching Mode Traditional lectures. Language Italian. AMS Campus. At the end of the course, the student knows the statistical laws that rule the thermodynamic behavior of macroscopic systems with a high number of particles and is able to describe the principal applications to both classical and quantum gases and to magnetic systems. We will study the theoretical bases of classical and quantum statistical mechanics.