Course data
Course name: Phase Transitions
Neptun ID: BMETE15MF63
Responsible teacher: Gergely Zaránd
Department: Department of Theoretical Physics
Programme: Courses for Physicist MSc students
Course data sheet: BMETE15MF63
Requirements, Informations

Phase Transitions (2020/21 Spring) 

Lecturers:  Gergely Zaránd and János Török
Time and location:    Lectures: Thursdays,  16:15-17:30, online course
Office hours: location and time will be specified later 
To join the course via Teams, please use the code: 5c01o0e
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:      The structure of the exam depends on the COVID situation. 
Problem solving: You can also obtain a grade through problem solving.
  • 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 (>=40 points); 3 (>=50 points); 4 (>=60 points); 5 (>=70 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 5 points/day.
  • Submisison  is planned to be through Teams Assigments.

Problems:     problems2019.pdf (grading and problems will be changed)

Handouts:    Will be handed out via Teams, tetatively before lectures... 

Subjects (tantative):
  1. Mean field theory, critical exponents, Ginzburg criterion
  2. Lower critical dimension, Goldstone modes.
  3. Hubbard-Stratonovic transformation, continuum theory, Goldstone modes large N limit
  4. The Basics of renormalization:  decimation the one dimensional Ising model, higher dimensions and critical point. 
  5. The two-dimensional Ising case: the generalized transformation, fixed points, critical surface, relevant and irrelevant operators. 
  6. Critical scaling all the free energy, universal exponents,  correlation functions of scaling operators 
  7. Finite size  scaling
  8. Quantum critical systems: discussion of the one-dimensional Ising chain.  Quantum classical mapping, higher dimensional phase diagrams.
  9. -||-
  10. Super fluidity and the XY model. Vortices and Kosterlitz-Thouless  phase transition.
  11. -||-
  12. Surface roughening
  13. -||-


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