Mathematical Statistical Mechanics (MAST90060)

Graduate courseworkPoints: 12.5On Campus (Parkville)

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Overview

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Semester 1
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The goal of statistical mechanics is to describe the behaviour of bulk matter starting from a physical description of the interactions between its microscopic constituents. This subject introduces the Gibbs probability distributions of classical and quantum statistical mechanics, the relations to thermodynamics and the modern theory of phase transitions and critical phenomena. The central concepts of critical exponents, universality and scaling are emphasized throughout. Applications include the ideal gases, magnets, fluids, one-dimensional Ising and Potts lattice spin models, random walks and percolation as well as approximate methods of solution.

Intended learning outcomes

After completing this subject students should be able to:

  • Describe how the ensembles and methods of classical and quantum statistical mechanics apply to a variety of problems in applied mathematics and mathematical physics;
  • Explain the role of critical phenomena in modern thermodynamics and use the principles of critical exponents, universality and scaling to examine the behaviour of complex systems;
  • Describe the basic concepts of phase transitions as applied to fluids, magnets, lattice spin models, random walks and percolation and use them to analyse such systems; and
  • Use the basic mathematical techniques of statistical mechanics including transfer matrices, real-space renormalization group and approximate methods to analyse a variety of systems.

Generic skills

In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:

  • Problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
  • Analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
  • Collaborative skills: the ability to work in a team; and
  • Time-management skills: the ability to meet regular deadlines while balancing competing commitments.

Last updated: 11 March 2025