Phase Transitions (2022/23 Spring)
Lecturers: Gergely Zaránd and Márton Kormos
Time and location: Lectures: Thursdays, 17:0018:30, 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

Mean field theory and its power

Wilsonian renormalization group 1: RG in one dimension

Wilsonian renormalization group 2: fixed points, relevant and irrelevant operators, RG and phase diagrams

Critical theory: correlations, scaling of free energy; finite size scaling

The field theoretical approach: HubbardStratonovic transformation, and the phi^4 theory.

RG in field theory, nonlinear sigma models.

Quantum criticality I: the transverse field Ising model.

Quantum criticality II: the quantumclassical mapping

Topological phase transitions

Superfluidity and the XY model. KosterlitzThouless phase transition

Ground state theorems for quantum spin systems

LargeN methods and spin liquids
Literature:

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 !