Course data
Course name: Phase Transitions and Criticality
Neptun ID: BMETE15MF48
Responsible teacher: Gergely Zaránd
Programme: Courses for Physicist MSc students
Course data sheet: BMETE15MF48
Requirements, Informations

Important! This is an obsolate course!

The current course id is BMETE15MF63.

Phase transitions (2018/19 Spring) 

Lecturers:  Gergely Zaránd and János Török
Time and location:  Thursday: 14:15-16:00, K376
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. 
Important infortmation: The final set of problems are out, the deadline is 18.06.2019. Delay penalty: 5points/day. (Days end at 4pm...).
Submission of solution: Electronically, through moodle systems.
Moodle accounts are created for each student. Moodle is available at Your username will be the same as your email name. Use the "Forgotten your username or password?" option to generate a new password which will be sent to you by email (if you already had an account just log in). Please submit each problem group to the corresponding moodle assignment. Note that there is a 6 MB limit for upload. Please make sure that your document fits into this limit.
On 24.06.2019 there will be a consultation at 10:00.
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 5 points to pass, but you cannot collect more than 30 points.
  • Grading is then as follows: 2 (>=31 points); 3 (>=41 points); 4 (>=56 points); 5 (>=71 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.
  • Out of  problems 1.1 and 1.2 only one can be submitted.

Problems: problems2019.pdf

Handouts:    Will come...

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: