Advanced Statistical Mechanics Lecture Notes

These are my lecture notes from the course Advanced Statistical Mechanics, taught by Prof. Mustansir Barma during the Fall 2025 semester at TIFR Hyderabad. The notes cover equilibrium statistical mechanics, phase transitions, critical phenomena, percolation theory, and renormalization group methods.

Lecture Notes

• Lecture 01: Introduction to Statistical Mechanics

• Lecture 02: Statistical Spin Models of Magnetism

• Lecture 03: Equivalence of Ensembles

• Lecture 04: Thermodynamic Potentials and Maxwell Relations

• Lecture 05: 1D Ising Model – Transfer Matrix Solution

• Lecture 06: General Prescription to Solve 1D Systems

• Lecture 07: Classical Heisenberg Spin Chain

• Lecture 08: Mean Field Solution of Ising Model and Matrix Inequalities

• Lecture 09: Variational Principle, Density Matrix and Ornstein–Zernike Theory

• Lecture 10: Ornstein–Zernike Theory and Introduction to Critical Phenomena

• Lecture 11: Critical Exponents, Scaling Hypothesis and Scaling Laws

• Lecture 12: Fluid–Magnet Analogy and Lattice Gas Model

• Lecture 13: Cluster Expansion of Interacting Gas Systems

• Lecture 14: Virial Expansion of Interacting Gas Systems

• Lecture 15: Spontaneous Ordering, Landau and Peierls Arguments

• Lecture 16: Ordering and Broken Symmetries

• Lecture 17: Spin Waves and Magnons

• Lecture 18: Phonons as Goldstone Modes, Q-Potts Model and Duality

• Lecture 19: Percolation Theory, Duality of Q-Potts and Random Cluster Models

• Lecture 20: Percolation in Bethe Lattice

• Lecture 21: Types of Percolation, Random Resistor Networks and Dilute Magnets

• Lecture 22: Introduction to Renormalization Group Theory

• Lecture 23: Linearization of RG Operator and RG Flow

• Lecture 24: RG Flow Curves and Universality Classes

• Lecture 25: Renormalization Group for One-Dimensional Models

• Lecture 26: Renormalization Group for the 2D Ising Model on the Triangular Lattice

• Lecture 27: Spin Weight Function and Momentum Space RG

• Lecture 28: Momentum Space RG for the Gaussian Model

• Lecture 29: Momentum Space RG for phi^4 Theory

Assignments

• Assignment 1: Heat-Capacity, Crystal Field Theory and Q-Potts Model

• Assignment 2: Ions in Lattice, Landau’s 1st order phase transition and Cluster Expansion of Tonks Gas