Outline:
1. Overview of Thermodynamics and Basic Statistical Mechanics
a. Fundamental equations
b. Microcanonical, canonical, and grand canonical ensembles
c. Connection formulas
2. The van der Waals Gas
a. Classical partition function
b. Configuration integral
c. Virial expansion
3. The Ising Model
a. Zero-field solution
b. The Ising model in a magnetic field
c. Correlation functions
4. Mean-Field Theory
a. Comparison between mean-field exponents and experimental measurements
b. Universality
c. Landau theory of phase transitions
5. Ginzburg-Landau Theory
a. Spatial correlations
b. Critical correlations
c. The Ginzburg criterion
6. The Scaling Hypothesis
a. Scaling form of the free energy
b. Scaling hypothesis for thermodynamic functions
c. Kadanoff block spin construction
7. The Renormalization Group in Real Space
a. Ising model in one dimension
b. Renormalization by decimation
c. Recursion relations and fixed points
8. Ising model in two dimensions
a. Decimation of the partition function
b. Recursion relations and fixed points
c. Scaling and critical exponents
Note: this outline is only indicative, some other relevant topics are to be added as lectures progress. The topic on renormalization group covers elementary notions, more on this topic will be taught in second semester (Check the syllabus for PHY716: Renormalization group and critical phenomena)