OVERVIEW

The main objective of the course is to to teach the fundamentals of statistical physics of out of equilibrium systems.  

AIMS AND CONTENT

LEARNING OUTCOMES

Verify and stimulate the basic knowledge on statistical physics. To take on recent arguments in the simplest possible context so to stimulate interest for the recent deveopments of statistical mechanics.

SYLLABUS/CONTENT

1.1 Phase transitions and critical phenomena

    Stages and phase diagram.

    Phase transitions.

    Critical phenomena.

    Scale transformations and renormalization group.

    Ising model

1.2 Theories of the average field

    Approximation of medium field.

    Critical exponents of the medium field theory.

    Landau theory.

    Infinite range model.

    Variational method.

    Ising antiferromagnetism model.

    Correlation function.

    Applicability limit of the average field theory.

    Critical dynamic phenomena.

    1

1.3 Renormalization and scaling group

    Coarse graining and scale transformations.

    Parameter space and renormalization group.

    Flow of the renormalization group near a fixed point and universality.

    Scale laws and critical exponents.

    Scale law for correlation and hyperscaling function.

    The one-dimensional Ising model.

    Theories of medium field and scale laws.

    Scale size and scale law.

    Scaling and anomalous dimensions.

1.4 Implementation of the renormalization group

    Group of renormalization in real space.

    Group of renormalization in the space of moments and development in ε.

1.5 Statistical physics of the fields

    From the bits to the fields.

    Continuous limit and field theory.

    Transformation of Hubbard-Stratonovich.

    Integration of degrees of freedom: coarse graining.

    Ginzburg-Landau phenomenological approach.

    Symmetry and its break.

    Ways of Nambu-Goldstone.

    Noether's theorem.

1.6 Conformable theories

• Overview.

2

1.7 The functional integral

• The integral of path in quantum mechanics. • The functional integral. The Gaussian model.
• Perturbation theory. Wick's theorem.

Reference texts: Nishimori-Ortiz: Elements of phase transitions and critical phe- nomena (Cap 1-5, excluding 2.8, 3.10-3.12, 4.3 and 5.8). Chapter 2 and 4 of DiFrancesco's book contain the part about path integrals, Wick's theorem and conformal theories.

The oral exam consists of the preparation of a paper and questions concerning the program.

RECOMMENDED READING/BIBLIOGRAPHY

Reference texts: Nishimori-Ortiz: Elements of phase transitions and critical phe- nomena (Cap 1-5, excluding 2.8, 3.10-3.12, 4.3 and 5.8). Chapter 2 and 4 of DiFrancesco's book contain the part about path integrals, Wick's theorem and conformal theories.

TEACHERS AND EXAM BOARD

Exam Board

NICODEMO MAGNOLI (President)

NICOLA MAGGIORE

PIERANTONIO ZANGHI'

LESSONS

Class schedule

STATISTICAL PHYSICS

EXAMS

EXAM DESCRIPTION

The oral exam is conducted by the main teacher and by another expert and it lasts from twenty to forty minutes.

ASSESSMENT METHODS

There are a fixed number of questions (the same for all students) that focus on the exam program so the commission can judge the preparation of the student and its autonomy.