Statistical Mechanics Course: Phases & Phase Transitions | Prof. V. Shenoy IISc
Course Details
| Exam Registration | 5 |
|---|---|
| Course Status | Ongoing |
| Course Type | Core |
| Language | English |
| Duration | 12 weeks |
| Categories | Physics |
| Credit Points | 3 |
| Level | Undergraduate/Postgraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 24 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Unlocking the Secrets of Matter: A Deep Dive into Phases and Phase Transitions
Why does ice melt into water? How do magnets form? What underlying principles govern the collective behavior of countless interacting particles, from molecules in a material to cells in a body? The answers lie in the profound and beautiful framework of statistical mechanics. This 12-week course, Statistical Mechanics of Phases and Phase Transitions, offered by Prof. Vijay Balakrishna Shenoy of the Indian Institute of Science (IISc) Bangalore, is designed to guide you through the core concepts that explain how matter organizes itself and transforms between different states.
Course Overview and Instructor Profile
This comprehensive course spans 12 weeks and is tailored for advanced undergraduate and postgraduate students. It builds from foundational principles to the cutting-edge applications of statistical mechanics in modern science.
The course is led by Prof. Vijay Shenoy, a distinguished professor of physics at IISc Bengaluru, where he has been a faculty member since 2002. Specializing in condensed matter theory, Prof. Shenoy brings deep expertise and a clear pedagogical approach to complex topics. You can find more about his research and work on his official webpage.
Who Should Take This Course?
This course is ideally suited for:
- Graduate students in physical sciences (Physics, Chemistry), chemical sciences, and engineering.
- Teachers and researchers looking for a structured refresher on advanced statistical mechanics.
Prerequisites: A solid foundation in Classical Mechanics, Quantum Mechanics, and elementary Statistical Mechanics at the graduate level is required to fully engage with the course material.
Detailed 12-Week Course Layout
The course is meticulously structured to take you from fundamental concepts to advanced theories and contemporary applications.
| Week | Topics Covered |
|---|---|
| Week 1 | Course Overview / Brief Review of Basics |
| Week 2 | Models, Symmetries, Scales, and Phases: Introduction to standard models (Ising, Heisenberg) and the concepts of symmetry and scale. |
| Week 3 | Characterization of Phases: Understanding broken symmetries, order parameters, and linear response theory. |
| Weeks 4 & 5 | Interacting Systems - Analysis Techniques: Studying imperfect gases, exact solutions (1D Ising model), and high-temperature expansions. |
| Week 6 | Numerical Methods: Hands-on exploration of the Monte-Carlo simulation method. |
| Week 7 | Landau-Ginzburg Theory: Diving into mean-field theory, Landau theory, and the role of fluctuations (including the Mermin-Wagner theorem). |
| Week 8 | Phase Transitions & Critical Phenomena: Exploring universal physics at critical points, the scaling hypothesis, and introduction to the renormalization group. |
| Week 9 | Renormalization Group (Deep Dive): Kadanoff's block-spin approach and Wilson's formulation of the renormalization group. |
| Week 10 | Near Lower Critical Dimensions: Examining the dramatic effects of fluctuations near the lower critical dimension. |
| Week 11 | Defect Mediated Transitions: Learning about topological defects and the Kosterlitz-Thouless theory. |
| Week 12 | Contemporary Applications: Fascinating case studies including quantum memories (topologically ordered states, toric code) and a statistical mechanics view of machine learning. |
Primary Reference Material
The course primarily follows the acclaimed text: Kardar, M., Statistical Physics of Fields, Cambridge University Press (2012, online edition available). This book is an excellent resource for deepening your understanding of the field-theoretic approaches to statistical mechanics covered in the later weeks.
Why Study Phases and Phase Transitions?
The concepts taught in this course form the bedrock of modern condensed matter physics and have far-reaching implications. Understanding phase transitions is not just about solids, liquids, and gases. It provides the language to describe:
- The emergence of magnetism and superconductivity.
- The behavior of complex systems in biology and economics.
- The stability of quantum information in topological quantum computing.
- The learning processes in neural networks, bridging physics and artificial intelligence.
By the end of this 12-week journey with Prof. Shenoy, you will have developed a powerful toolkit to analyze how order emerges from disorder, how systems behave at their critical points, and how these century-old ideas are driving today's most exciting scientific and technological frontiers.
Enroll Now →