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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.

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. Huang, Statistical Mechanics; L. Landau and E. Lifshitz, Statistical Physics, Part 1; L. Kadanoff, Statistical Physics.

Statics, Dynamics and Renormalization, D. Landau and K. 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. Skip to main content. Corso di Second cycle degree in Physics. Academyc year when starting the degree:. Academyc year when helding the course:. Course type:. Compulsory subjects, characteristic of the class.

Standard lectures hours:. Basic principles of classical and quantum statistical mechanics.

LEY 26743 PDF

31552 - Statistical Mechanics 1

Information on the course unit. ECTS: details. Course unit organization. Prerequisites: Statistical Mechanics course given at the third year of the laurea triennale Thermodynamics Target skills and knowledge: After completing the course the student should be able to understand and explain the basic concepts and the use of advanced techniques in statistical mechanics.


Meccanica Statistica Elementare : I Fondamenti

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