### Sciences

## Subject: STATISTICAL MECHANICS AND PHASE TRANSITIONS (A.A. 2020/2021)

### master degree course in PHYSICS – FISICA

Course year | 1 |
---|---|

CFU | 6 |

Teaching units |
Unit Statistical Mechanics and Phase Transitions
Microphysics and Material Structure (lesson)
- TAF: Compulsory subjects, characteristic of the class SSD: FIS/03 CFU: 6
Guido GOLDONI |

Exam type | oral |

Evaluation | final vote |

Teaching language | English |

### Teachers

### Overview

To learn the formal methods of classical and quantum statistical mechanics of interacting systems and phase transitions and recognize the advantages and limitations of the different methods.

To apply the formal methods to selected classes of classical and quantum statistical systems and describe their phenomenologies.

To acquire the correct use of the specific language and description of modern statistical mechanics and phase transitions.

### Admission requirements

The fruitful attendance of the course requires the acquisition of the main concepts of classic and quantum mechanics, elementary statistical mechanics of ideal systems, and the structure of matter which are conveyed by the three years degree in physics.

### Course contents

Kinetic theory and Boltzmann equation - H-Theorem and irreversibility - Quantum statistics and density matrix - Phase diagram of fluids, magnetic systems and other physical systems - The problem of condensation and the virial expansion - Spin models - The Ising model: mean field solution - Critical exponents - Correlations - Landau function - Order parameter and spontaneous symmetry breaking - The scaling hypothesis - Statistical field theories - Fluctuations and Gaussian approximation - Continuous symmetry systems and Goldstone modes - Critical dimensions - Kosterlitz-Thouless transition - Renormalization group method - Bosonic condensates - Superfluidity - Superconductivity - Ginburg-Landau theory - BCS theory of superconductivity

### Teaching methods

Lectures on formal methods, exercises in the classroom.Slides containing graphs discussed during classes and texts of the exercises are distributed via Dolly. For working students: students who can not attend classes must notify the teacher to receive specific guidance on the subjects to be studied on the suggested books and teaching materials possibly distributed. Meeting with the teacher: by appointment obtained by e-mail

### Assessment methods

Final oral examination with discussion on the main topics and discussion of a research paper assigned by the teacher (optional).

### Learning outcomes

Competence and understanding

Ability to understand the fundamental phenomenology and the modern interpretation of statistical physics, phase transitions and critical phenomena.

Ability to apply knowledge and understanding

Ability to acquire specific autonomous skills and to analyze the applications of physics of statistical systems in the context of condensed matter physics.

Independent thinking.

Ability to orientate oneself and recognize the advantages and limitations of the main methods of statistical physics.

Communication skills.

Understanding the scientific literature in the field of statistical physics and phase transitions, recognizing the main methodological elements and outlining the results correctly and precisely.

Ability to acquire new knowledge.

Ability to evaluate their skills in the context of current knowledge and research in the sector, to expand and deepen their training using the main field monographs and scientific literature.

### Readings

Recommended textbooks

H. E. Stanley - Introduction to phase transitions and critical phenomena - Clarendon Press (Oxford, 1971)

R. K. Pathria - Statistical mechanics, 2nd edition - Butterworth Heinemann (Oxford, 1996)

D. Chandler - Introduction to Modern Statistical Mechanics Oxford University Press (USA, 1987)

N. Goldenfeld - Lectures on Phase Transitions and the Renormalization Group (Frontiers in Physics, Westview Press)

J. F. Annet - Superconductivity, superfluids and condensates (Oxford University Press, 2004)