Lectures on the Ising and Potts model

Solutions to exercises given in Hugo Duminil Copin’s notes on the Ising model. The compiled solutions are HERE.

Chapter 1: Graphical representation of the Potts model.

• Exercise 7 (First Griffiths Inequality)
• Exercise 8 (Second Griffiths Inequality)
• Exercise 9 (Comparison with boundary conditions 1)
• Exercise 10 (Comparison with boundary conditions 2)

Chapter 2: Computation of critical points and sharp phase transitions.

• Exercise 22 (Square root trick)
• Exercise 23 (Zhang’s Argument)

Chapter 4: Continuity of the phase transition for the Ising model.

Chapter 5: Continuity/Discontinuity of the phase transition for the planar random-cluster model.

Chapter 6: Conformal invariance of the Ising model on \(\mathbb{Z}^2.\)