Outline

• Spin models: Ising, XY, Heisenberg
• Mean field approximation for magnets
• Mean field critical exponents
• 1D Ising model: exact solution
• 1D Ising model: spin correlations
• 2D Ising model: free energy argument

Scope

To point out limitations of the mean-field approximation in predicting the transition temperature and the critical exponents in low dimensions, by comparing with the exact solutions for the Ising model in 1D and 2D.