Explore why matter can exist in more than one phase, and how it can transform from one phase into another. Develop the ideas of entropy, free energy and thermal equilibrium starting from the question “what is temperature?”. From the context of thermodynamics, and as natural consequences of a statistical description of matter, develop a simple physical picture of phase transitions with an emphasis on the unifying concept of broken symmetry. Demonstrate understanding of the subject through weekly problem sets, and deliver a final presentation on a modern example of the application of statistical physics ideas, chosen by the student. Accessible to students from a wide range of education backgrounds.
This course introduces the fundamental concepts and mathematical techniques of equilibrium statistical mechanics in the context of two simple questions: Why does matter exist in different phases ? And how does it change from one phase to another?
- General overview of phase transitions - what are they, and where do they happen?
- Introduction to the basic concepts of thermodynamics - temperature, entropy, thermodynamic variables and free energy - through the example of an ideal gas.
- Introduction to the basic concepts and techniques of statistical mechanics - phase space, partition functions and free energies. How can we calculate the properties of an ideal gas from a statistical description of atoms?
- Introduction to the idea of a phase transition. How does an non-ideal gas transform into a liquid?
- The idea of an order parameter, distinction between continuous and first order phase transitions and critical end points. How do we determine whether a phase transition has taken place?
- Magnetism as a paradigm for phase transitions in the solid state - the idea of a broken symmetry and the Landau theory of the Ising model.
- Universality - why do phase transitions in fluids mimic those in magnets? An exploration of phase transitions in other universality classes, including superconductors and liquid crystals.
- Alternative approaches to understanding phase transitions: Monte Carlo simulation and exact solutions.
- How does one phase transform into another? Critical opalescence and critical fluctuations. The idea of a correlation function.
- The modern theory of phase transitions - scaling and renormalization.
- To be developed through student presentations: modern applications of statistical mechanics, with examples taken from life-sciences, sociology, and stock markets.
Weekly problem sheets 75%. Final presentation 25%
- F. Mandl, “Statistical Physics”, 2nd Edition (1988) Wiley
- K. Huang, “Introduction to Statistical Physics” 2nd Edition - (2009) Chapman & Hall
- M. Plischke and B. Bergersen, “Equilibrium Statistical Mechanics” 3rd edition (2006) World Scientific
- "L. D. Landau and E. M. Lifshitz, “Statistical Physics” (1996) Butterworth-Heinermann
- P. Chaikin and T. Lubensky, “Principles of Condensed Matter Physics” (2003) Cambridge University Press"
Undergraduate calculus and algebra.