Elementary scattering theory; symmetry, order and phase transitions. Correlation functions in classical systems; order parameter and models. Mean field theory: First and second order transitions. Critical exponents, universality and scaling laws. Renormalization Group and critical phenomena.
Choice among: i) Dynamic correlations; ii) Spin models and magnetic excitations; iii) Introduction to Monte Carlo simulations; iv) Topological transitions in 2 dimensions.
P.M. Chaikin and T.C. Lubensky. Principles of condensed matter physics, Cambridge University Press.
N.W. Ashcroft and N.D. Mermin, Solid State Physics, Holt, Rinehart and Winston.
Learning Objectives
Knowledge acquired:
Physics of critical phenomena. Universality. Renormalization group. Magnetic properties of insulating materials and spin models; Spin waves. Static and dynamic correlations in condensed matter and elastic and inelastic scattering experiments. Numerical simulation methods of thermodynamic systems.
Competence acquired :
Evaluation of simple static structure factors. Evaluation of mean-field critical temperature and RPA corrections. Renormalization-group evaluation of critical exponents at first order in epsilon in reciprocal space. Evaluation of susceptibility, spin-wave frequency and magnetic excitation contribution to low-T thermodynamic properties of localized spin models.
Skills acquired (at the end of the course):
Characterization of scaling and universal behavior as well as non-universal properties in phase transitions. Characterization of different contributions, especially magnetic ones, to the thermodynamic properties of insulating materials. Interpretation of elastic and inelastic scattering experiments in condensed matter.
Teaching Methods
6 CFU
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 150
Contact hours for: Lectures (hours): 48
Further information
Office hours
Wednesday 11:00-13:00.
May vary each academic year; please check on web page
Website
http://www.fi.infn.it/cmtg/ac/
Type of Assessment
Oral discussion
Course program
Elementary scattering theory: gases, liquids, solids; symmetry and crystal structure; one- and two-dimensional order. Elements of thermodynamics and Statistical Mechanics; correlation functions in classical systems; symmetry, order parameter and models. Mean field theory: Landau theory of phase transitions; first and second order transitions. Critical exponents, universality and scaling laws. Renormalization Group and critical phenomena.
Choice among following topics: i)
Dynamic correlations and inelastic scattering; ii) Magnetic systems and spin models: excitations and thermodynamic properties; iii) Introduction to Monte Carlo numerical simulations; iv) Continuous symmetries and topological transitions in two dimensions.