Degree course: 
Corso di Second cycle degree in Physics
Academic year when starting the degree: 
Academic year in which the course will be held: 
Course type: 
Compulsory subjects, characteristic of the class
Second semester
Standard lectures hours: 
Detail of lecture’s hours: 
Lesson (48 hours)

Basic principles of classical and quantum statistical mechanics.

Voto Finale

The purpose is to illustrate the theoretical approach to the analysis of critical phenomena through the renormalization group theory in real space. We will also introduce numerical algorithms for the analysis of critical properties. We expect an in- depth understanding of this topics.

Ising model. Absence of phase transition in one dimension: free energy argument and exact solution with transfer matrices. Peierls’ argument in two dimensions, Bragg-Williams and Bethe-Peierls approximations. Kramers-Wannier duality. Exact solution in two dimensions. Fluctuation dissipation theorem. Widom Scaling and scale relations. Correlation functions and extension of mean field theory. General formulation of the renormalization group in real space. Scaling of free energy and relevant eigenvalues. Ising model on a triangular bidimensional lattice: renormalization at lowest cumulant order. Renormalization of a Potts model on a hierarchical lattice. Monte Carlo methods: Markovian stochastic processes, detailed balance, ergodicity. Spin flipping: Metropolis algorithm. Cluster flipping: Fortuin Kasteleyn transformation, the cluster count Hoshen-Kopelman alogorithm, and Swendsen-Wang algorithm.
Lectures, including the illustration of the theory, and applications.

K. Huang, Statistical Mechanics; L.D. Landau and E.M. Lifshitz, Statistical Physics, Part 1; L.P. Kadanoff, Statistical Physics. Statics, Dynamics and Renormalization, D. Sornette, Critical Phenomena in Natural Sciences, L.E. Reichl, A Modern Course in Statistical Physics, D.P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics.
Students have access to transcripts of lectures on the homepage of the professor, and it is possible to stream on demand recording of lessons.
Final oral examination with discussion of topics related to course program and related exercises.