Tantárgy adatok
Tárgy címe: Fázisátalakulások és kritikus jelenségek
Neptun kód: BMETE15MF48
Felelős oktató: Dr. Zaránd Gergely
Felelős tanszék: Elméleti Fizika Tanszék
Képzés: MSc fizikus
Tantárgy adatlapja: BMETE15MF48
Követelmények, Információk

Phase transitions (2016/17 Spring) 

Lecturers:  Gergely Zaránd and János Török
Time and location:  T: 12:15-14:00, location to be specified
                                  First lecture on february 14!
Office hours: once in every three weeks, location and time will be specified later 
Language of course: English, discussions can be in Hungarian, exams can be taken in Hungarian, too. 
Grading:    There are two ways to pass. 
Oral exam:      Everyone receives two subjects, from a list of subjects.
List of subjects (will be given later)
Problem solving: You can also obtain a grade through problem solving, but to take this opportunity, you 
must be present at least at 80% of the lectures (i.e., you can miss 2 lectures).
  • You shall receive 4 problem sets in course of the semester. 
  • From each set you must collect at least 10 points to pass, but you cannot collect more than 30 points.
  • Grading is then as follows: 2 (>=50 points); 3 (>=60 points); 3 (>=70 points); 4 (>=80 points); 5 (>=90 points).
  • You are allowed to discuss with others and ask for help with the lecturers in case you are stuck, but we request independent work. In other words, you can help others and exchange sometimes ideas, but you are NOT allowed to copy. 
  • Deadlines shall be specified within each set. Delay implies a loss of 2 points/day.

Handouts:    Will come...

Subjects (tantative):
  1. First and second order phase transitions, correlation legnth, self-similarity and universality. Few typical phase transitions (Uniaxial magnets, uniaxial magnets in perpendicular fields, Mott transition, dyanamical phase transitions, localization phase transition). 
  2. Mean field theory, critical exponents, Ginzburg criterion. 
  3. Symmetres and Landau-theory.  Applications to simple systems, coupled order parameters.
  4. Basics of renormalization: decimation, the case of the 1-dimensional Ising model, higher dimensions and existance of a critical point.
  5. Wilson's renormalization group structure: fixed points, critical surface, relevant and irrelevant operators. 
  6. Critical scaling of free energy and universal exponents, correlation functions of scaling operators. Scaling near the critical point.
  7. Finite size scaling and first order transitions. 
  8. Quantum critical systems: one-dimensional Ising chain.
  9. The quantum-classical mapping, typical quantum phase diagrams.
  10. Superfluidity and the XY model. Vortices and  the Kosterlitz-Thouless phase transition.
  11. Hubbard-Stratonovic transformation and continuum field theories. Goldstone-modes and large n limit.
  12. Quantum magnets and spin liquids. 
  13. Topological phase transitions.


  • John Cardy: Scaling and Renormalization in Statistical Physics (Cambridge University Press, 1996).
  • Subir Sachdev, Quantum Phase Transitions, Cambridge University Press (2011). 
Supplementl Material: