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. The critical phenomena constitute the classical 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 by multiple addresses.
The remaining 2 credits focus on Monte Carlo methods and molecular dynamics in the study of phase equilibria and rare events with applications in the physics of matter.
The remaining 2 credits focus on Monte Carlo methods and molecular dynamics in the study of phase equilibria and rare events with applications in the physics of matter.
Curriculum
teacher profile teaching materials
Brief mention of main concepts of thermodynamics. The thermodynamic potentials.
Phase transitions and the van der Waals equation for the real gases. Fluctuations and thermodynamic stability.
Quantum theory of linear response.
Phase transitions and thermodynamic limit.
Microscopic derivation of the van der Waals equation and its behavior at the critical point.
The Curie-Weiss theory of the ferromagnetic transition.
The Landau theory of the second order phase transitions.
The Ginzburg criterion for the validity of the mean-field approach.
The role of symmetry and of dimensionality in the phase transitions: the Mermin-Wagner theorem.
The Kadanoff-Wilson transformation for the renormalization group.
Evaluation of the fixed points in the Landau-Wilson model and epsilon expansion.
II unit (2 CFU)
The standard model of metals: disordered electron systems.
The weak localization concept and the metal-insulator transition.
Superconductivity.
by Carlo Di Castro and Roberto Raimondi
Cambridge University Press 2015
ISBN: 9781107039407
Programme
I unit (6CFU)Brief mention of main concepts of thermodynamics. The thermodynamic potentials.
Phase transitions and the van der Waals equation for the real gases. Fluctuations and thermodynamic stability.
Quantum theory of linear response.
Phase transitions and thermodynamic limit.
Microscopic derivation of the van der Waals equation and its behavior at the critical point.
The Curie-Weiss theory of the ferromagnetic transition.
The Landau theory of the second order phase transitions.
The Ginzburg criterion for the validity of the mean-field approach.
The role of symmetry and of dimensionality in the phase transitions: the Mermin-Wagner theorem.
The Kadanoff-Wilson transformation for the renormalization group.
Evaluation of the fixed points in the Landau-Wilson model and epsilon expansion.
II unit (2 CFU)
The standard model of metals: disordered electron systems.
The weak localization concept and the metal-insulator transition.
Superconductivity.
Core Documentation
Statistical Mechanics and Applications in Condensed Matterby Carlo Di Castro and Roberto Raimondi
Cambridge University Press 2015
ISBN: 9781107039407
Type of evaluation
final oral examination teacher profile teaching materials
Brief mention of main concepts of thermodynamics. The thermodynamic potentials.
Phase transitions and the van der Waals equation for the real gases. Fluctuations and thermodynamic stability.
Quantum theory of linear response.
Phase transitions and thermodynamic limit.
Microscopic derivation of the van der Waals equation and its behavior at the critical point.
The Curie-Weiss theory of the ferromagnetic transition.
The Landau theory of the second order phase transitions.
The Ginzburg criterion for the validity of the mean-field approach.
The role of symmetry and of dimensionality in the phase transitions: the Mermin-Wagner theorem.
The Kadanoff-Wilson transformation for the renormalization group.
Evaluation of the fixed points in the Landau-Wilson model and epsilon expansion.
II unit (2 CFU)
The standard model of metals: disordered electron systems.
The weak localization concept and the metal-insulator transition.
Superconductivity.
by Carlo Di Castro and Roberto Raimondi
Cambridge University Press 2015
ISBN: 9781107039407
Mutuazione: 20401425 MECCANICA STATISTICA in Fisica LM-17 N0 RAIMONDI ROBERTO
Programme
I unit (6CFU)Brief mention of main concepts of thermodynamics. The thermodynamic potentials.
Phase transitions and the van der Waals equation for the real gases. Fluctuations and thermodynamic stability.
Quantum theory of linear response.
Phase transitions and thermodynamic limit.
Microscopic derivation of the van der Waals equation and its behavior at the critical point.
The Curie-Weiss theory of the ferromagnetic transition.
The Landau theory of the second order phase transitions.
The Ginzburg criterion for the validity of the mean-field approach.
The role of symmetry and of dimensionality in the phase transitions: the Mermin-Wagner theorem.
The Kadanoff-Wilson transformation for the renormalization group.
Evaluation of the fixed points in the Landau-Wilson model and epsilon expansion.
II unit (2 CFU)
The standard model of metals: disordered electron systems.
The weak localization concept and the metal-insulator transition.
Superconductivity.
Core Documentation
Statistical Mechanics and Applications in Condensed Matterby Carlo Di Castro and Roberto Raimondi
Cambridge University Press 2015
ISBN: 9781107039407
Type of evaluation
final oral examination