A.A. 2017-2018

Statistical Physics 2

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Structure of the course: there will be a set of “common” lectures on the theory of critical phenomena and real space renormalization group. Besides that, each student will work on a final project on a different subject, to be selected together with me: I will provide appropriate references for such “advanced issues”.

Reference books: K. Huang, Statistical Mechanics (KH); L.D. Landau and E.M. Lifshitz, Statistical Physics, Part 1 (LL); L.P. Kadanoff, Statistical Physics. Statics, Dynamics and Renormalization (LK), D. Sornette, Critical Phenomena in Natural Sciences (DS), L.E. Reichl,

A Modern Course in Statistical Physics (LR), D.P. Landau and K. Binder, A Guide to Monte

Carlo Simulations in Statistical Physics (LB), G. Mussardo, Il modello di Ising (GM), G.A. Baker, Jr., Quantitative theory of critical phenomena (GB), H. Nishimori and G. Ortiz, Elements of Phase Transitions and Critical Phenomena (NO), R.J. Baxter, Exactly Solved Models in Statistical Mechanics (Ba)

Updated iPad screens (some lectures are missing) pdf

Updated list of available lessons (streaming on demand)  link  (starting march, 10;

former lectures refer to Statistical Physics 1)

Syllabus (common part) - Canard du jour

08-3-2018 - Introduction

15-3-2018 - General features of Ising model. 1d exact solution, absence of a phase

                   transition. [KH,GM]

16-3-2018 - Peierls argument. [KH]

22-3-2018 - Bragg-Williams and Bethe-Peierls approximations. [KH]

23-3-2018 - Kramers-Wannier duality. [Ba]

05-4-2018 - Exact solution of 2d Ising in zero field (part 1). [LL]

06-4-2018 - Exact solution of 2d Ising in zero field (part 2). [LL]

12-4-2018 - Fluctuation dissipation theorem. Widom scaling. [KH]

19-4-2018 - Ornstein Zernike estimate of the critical exponents for correlation

                   functions [LK]

20-4-2018 - The gaussian model [GM]

26-4-2018 - Real space renormalization group: general formalism 1

27-4-2018 - Real space renormalization group: general formalism 2

03-5-2018 - Renormalization of 2d Ising on a triangular lattice

04-5-2018 - Renormalization of Potts model on a diamond lattice

17-5-2018 - The central limit theorem via renormalization group [DS]

18-5-2018 - Mermin Wagner theorem; spin wave approximation of the vector model [NO]

Meccanica analitica

Testi di riferimento: Goldstein, Poole, Safko: Classical mechanics (Go); Landau: Meccanica (La); Lowenstein: Essentials of hamiltonian dynamics (Lo); Arnold: Mathematical methods of classical mechanics (Ar); Sommerfeld: Mechanics (So); Corben: Classical mechanics (Co);

Gutzwiller: Chaos in classical and quantum mechanics (Gu).

Note iPad aggiornate pdf

Le registrazioni delle lezioni sono disponibili al seguente link

Sunto delle lezioni:

26-09-2017 -- Presentazione del corso. Alcuni richiami di meccanica elementare.

27-09-2017 -- Altri richiami di meccanica elementare. Principio di D’Alembert.

03-10-2017 -- Dal principio di D’Alembert alle equazioni di Lagrange.

04-10-2017 -- Esempi: particella in coordinate polari, pendolo doppio.

                      Variabili cicliche.

10-10-2017 -- Particella carica in un campo elettromagnetico: potenziale generalizzato.

11-10-2017 -- Calcolo delle variazioni ed equazioni di Eulero-Lagrange. Principio di

                      Hamilton. Geodetiche nel piano e sulla sfera.

12-10-2017 -- Esercitazioni. Testo degli esercizi.

17-12-2017 -- Principio di Hamilton in presenza di vincoli semiolonomi. Teorema di

                      Noether lagrangiano.

18-10-2017 -- Conservazione dell’energia. Carattere piano per il moto in presenza di

                      forze centrali.

24-10-2017 -- Il problema di Keplero.

25-10-2017 -- Lo scattering di Rutherford.

31-10-2017 -- Teorema del viriale. Cinematica del corpo rigido.

02-11-2017 -- Esercitazioni. Testo degli esercizi.

07-11-2017 -- Velocità angolare nella terna del laboratorio e nella terna mobile.

08-11-2017 -- Terne principali d’inerzia, energia cinetica.

14-11-2017 -- Moto libero di una trottola simmetrica.

15-11-2017 -- La trottola di Lagrange. Trottola dormiente. Piccole oscillazioni

                      attorno a posizioni di equilibrio: frequenze proprie.

16-11-2017 -- Esercitazioni. Testo degli esercizi.

21-11-2017 -- Vibrazioni proprie della molecola di CO2.

22-11-2017 -- Momenti generalizzati ed equazioni di Hamilton.

28-11-2017 -- Hamiltoniana in sistemi di riferimento ruotanti, e di una particella

                      carica in un campo elettromagnetico.

29-11-2017 -- Da Lagrange a Hamilton attraverso la ttasformazione di Legendre.

30-11-2017 -- Esercitazioni. Testo degli esercizi.

05-12-2017 -- Trasformazioni canoniche (funzioni generatrici).

06-12-2017 -- Trasformazioni canonicha (parentesi di Poisson).

12-12-2017 -- Trasformazioni canoniche infinitesime.

13-12-2017 -- Simmetrie e leggi di conservazione.

14-12-2017 -- Esercitazioni. Testo degli esercizi.

19-12-2017 -- La teoria di Hamilton Jacobi (1).

09-01-2018 -- La teoria di Hamilton Jacobi (2). Separabilità.

10-01-2018 -- Moto planare in presenza di un doppio centro. Azione come funzione

                      delle coordinate.

17-01-2018 -- Esercitazioni. Testo degli esercizi.

Statistical Physics 1

Prerequisites: Classical and Quantum Mechanics. Elementary notions of Thermodynamics and Probability Theory.

Suggested reference books: K. Huang, Statistical Mechanics (KH); M. Kardar, Statistical Physics of Particles (MK); L.D. Landau and E.M. Lifshitz, Statistical Physics, Part 1 (LL); L.E. Reichl, A Modern Course in Statistical Physics (LR).

Supplementary reading: A. Sommerfeld, Thermodynamics and Statistical Mechanics (AS); A.I. Khinchin, Mathematical Foundations of Statistical Mechanics (Kh); C.J. Thompson, Classical Equilibrium Statistical Mechanics (CT); J.M. Yeomans, Statistical Mechanics of Phase Transitions (JY); M. Plischke and B. Bergersen, Equilibrium Statistical Physics (PB), J.P. Sethna, Entropy,

Order Parameters and Complexity (JS) web book, P.M. Chaikin and T.C. Lubensky, Principles

of Condensed Matter Physics (CL), R. Balian, From Microphysics to Macrophysics, Vol. 1 (RB),

G.H. Wannier, Statistical Physics (GW), F. Reif, Fundamentals of Statistical and Thermal Physics

(FR), E.A Guggenheim, Thermodynamics (EG).

Updated iPad screens pdf

Lectures available for streaming on demand  link (the course consists of lectures 1 to 15)


11-10-2017 -- Introduction to the course.

13-10-2017 -- The thermodynamic description. First and second principles.

18-10-2017 -- Relationships among response functions.

19-10-2017 -- Third law. Coexistence curve and Clausius-Clapeyron equation.

25-10-2017 -- Van der Waals’ equation of state.

26-10-2017 -- Critical exponents. Landau theories.

02-11-2017 -- Phase space densities: Liouville equation.

08-11-2017 -- Rudiments of ergodic theory. Khinchin’s inequality. Microcanonical


09-11-2017 -- From microcanonical to canonical ensemble.

15-11-2017 -- Model for a Van der Waals gas. Grand canonical ensemble.

16-11-2017 -- Adsorption. Number fluctuations in the grand canonical ensemble.

23-11-2017 -- The existence of the thermodynamic limit.

29-11-2017 -- Quantum Gibbs ensembles.

30-11-2017 -- The classical limit of the quantum partition function.

06-12-2017 -- Virial and cluster expansions.

13-12-2017 -- Fermi gas (1).

20-12-2017 -- Fermi gas (2).

21-12-2017 -- Pauli paramagnetism.

10-01-2018 -- Landau diamagnetism. Debye theory.

11-01-2018 -- Bose Einstein condensation.