STATISTICAL PHYSICS II
- Scheda dell'insegnamento
- Obiettivi formativi
- Metodi didattici
- Verifica dell'apprendimento
- Altre informazioni
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, as well as the ability to read original papers in this framework.
Basic principles of classical and quantum statistical mechanics.
Ising model. [12h]
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.
Correlations and scaling. [6h]
Fluctuation dissipation theorem. Widom Scaling and scale relations. Correlation functions and extension of mean field theory.
Renormalization group. [20h]
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.
Introduction to Monte Carlo methods. [10h]
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.
The course consists of frontal lectures.
The final examination consists of an oral interview, where the student is asked to describe in a quantitative way the proposed arguments, emphasising the physically relevant results. The student has to also to prepare a talk on an original paper, chosen together with the lecturer.
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.
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