20401425 - STATISTICAL MECHANICS

The course aims to give an overview of modern developments in statistical mechanics. In particular, starting from the theory of phase transitions and critical phenomena, we want to show how the concepts underlying the renormalization group method emerged. This method is now widely used in various fields of statistical mechanics. Critical phenomena constitute the classic application of the method, which is illustrated in detail in the first 6 credits of the course. These first 6 credits can therefore be used from multiple addresses.

The remaining 2 credits focus on spin glasses and the study of phase equilibria and rare events with applications in condensed matter phy

LUPI LAURA

teacher profile | teaching materials

Programme

1st module program (6 credits)

Introduction to thermodynamics.
Thermodynamic potentials.
Phase transitions and Van der Waals equation.
Fluctuations and stability.
Phase transitions and thermodynamic limit.
Microscopic derivation of the Van der Waals equation.
Critical point behavior of the Van der Waals equation.
Curie-Weiss theory of ferromagnetism.
Landau theory of second species transitions.
Ginzburg criterion for the validity of the middle field theory.
The role of symmetry and dimensionality: the Mermin-Wagner theorem.
Renormalization team.
Kadanoff-Wilson transformation.
Calculation of fixed points for the Landau-Wilson model and development in epsilon.

II module program (2 credits)

Spin glasses
Methods for calculating free energy.
Advanced techniques for simulating rare events.


Core Documentation

Statistical Mechanics and Applications in Condensed Matter
by Carlo Di Castro and Roberto Raimondi
Cambridge University Press 2015
ISBN: 9781107039407

Type of delivery of the course

frontal lessons on the blackboard

Type of evaluation

Final oral exam

LUPI LAURA

teacher profile | teaching materials

Programme

1st module program (6 credits)

Introduction to thermodynamics.
Thermodynamic potentials.
Phase transitions and Van der Waals equation.
Fluctuations and stability.
Phase transitions and thermodynamic limit.
Microscopic derivation of the Van der Waals equation.
Critical point behavior of the Van der Waals equation.
Curie-Weiss theory of ferromagnetism.
Landau theory of second species transitions.
Ginzburg criterion for the validity of the middle field theory.
The role of symmetry and dimensionality: the Mermin-Wagner theorem.
Renormalization team.
Kadanoff-Wilson transformation.
Calculation of fixed points for the Landau-Wilson model and development in epsilon.

II module program (2 credits)

Spin glasses
Methods for calculating free energy.
Advanced techniques for simulating rare events.


Core Documentation

Statistical Mechanics and Applications in Condensed Matter
by Carlo Di Castro and Roberto Raimondi
Cambridge University Press 2015
ISBN: 9781107039407

Type of delivery of the course

frontal lessons on the blackboard

Type of evaluation

Final oral exam