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

Phase Transitions (2022/23 Spring) 

Lecturers:  Gergely Zaránd and Márton Kormos
Time and location:    Lectures: Thursdays,  17:00-18:30, Tutorials: 18:35 - 19:15 
To join the course via Teams, please use the code: k7mp9tt
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:      This is open to everyone, and  there is no course attendence requirement for this. 
Problem solving: You can also obtain a grade through problem solving in case you do not miss more than two lectures during the semester.
  • You will 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 from one set.
  • 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 from 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.
  • Submisison  is planned to be through Teams Assigments.

Problems:     problems2019.pdf (just for reference, grading and problems will be changed)

Handouts:    Will be handed out via Teams.

Subsects for oral exam:  Subjects_for_PhaseTransitions_exam 2023.docx

Subjects (tentative in 2023): detailed schedule
  1. Mean field theory and its power
  2. Wilsonian renormalization group 1: RG in one dimension
  3. Wilsonian renormalization group 2:  fixed points, relevant and irrelevant operators, RG and phase diagrams
  4. Critical theory: correlations, scaling of free energy; finite size scaling 
  5. The field theoretical approach: Hubbard-Stratonovic transformation, and the phi^4 theory.
  6. RG in field theory, nonlinear sigma models. 
  7. Quantum criticality I: the transverse field Ising model.  
  8. Quantum criticality II: the quantum-classical mapping
  9. Topological phase transitions
  10. Superfluidity and the XY model. Kosterlitz-Thouless  phase transition
  11. Ground state theorems for quantum spin systems
  12. Large-N methods and spin liquids 


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