Statistical mechanics of phase transitions

• Introduction
• Statistical mechanics and phase transitions
• Long range correlations
• Finite size effects on phase transitions
• Models in statistical mechanics
• The Ising model - Introduction
• Analytic properties of the Ising model
• Absence of phase transitions for finite systems
• Ising model and fluids
• Ising model and the ideal gas
• Ising model and binary alloys
• Ising model and neural networks
• Final remark on equivalence in statistical mechanics
• Ising model in one dimension
• Bulk free energy, thermodynamic limit and absence of phase transitions
• Irrelevance of boundary conditions
• Absence of spontaneous magnetization
• The transfer matrix method
• A slightly trickier system: the Heisenberg model
• The Ising model in higher dimensions
• Additional remarks on the Ising model
• The role of dimensionality
• The role of symmetry
• The role of interaction range