
Course unit
STATISTICAL MECHANICS
SCP7081659, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
FIS/02 
Theoretical Physics, Mathematical Models and Methods 
6.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
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.
2) Understand the use of partition functions and their relation with thermodynamics
3) Explain the concept of phase transitions in simple models as well as the physics at or near critical points.
4) Understand the role of dimension and range of interaction in phase transitions
5) Apply the theory of scaling and the renormalisation group to simple systems
6) Understand the strength and limitation of the models
7) Show an analytic ability to solve problems relevant to statistical physics 
Examination methods:

The verification of the acquired knowledge takes place through a common written test with 12 exercises to be solved analytically and 12 open questions on basic concepts. 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. Universality.
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. 
Additional notes about suggested reading:

All the teaching material used for lectures (blackboard lessons, case study articles, review of the content of the recommended texts) is made available to students in pdf format on the elearning platform: https: // elearning. unipd.it/ 
Textbooks (and optional supplementary readings) 

K. Huang, Meccanica Statistica. : Zanichelli, .

L. Peliti, Statistical Mechanics in a Nutshell. : Princeton, .

J. Yeomans, Statistical mechanics of Phase transitions. Oxford: Oxford University Press, 1992.

Sustainable Development Goals (SDGs)

