Unit name | The Physics of Phase Transitions. |
---|---|

Unit code | PHYSM0300 |

Credit points | 10 |

Level of study | M/7 |

Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |

Unit director | Dr. Machon |

Open unit status | Not open |

Pre-requisites |
PHYS30021 Solid State Physics 302, or MATH34300 Statistical Mechanics. |

Co-requisites |
None. |

School/department | School of Physics |

Faculty | Faculty of Science |

This courses employs the fundamental concepts and mathematical techniques of equilibrium statistical mechanics, to address two simple questions: Why does matter exist in different phases? And how does it change from one phase to another?

Aims:

Matter can exist in many different phases. The aim of this course is to develop a physical and mathematical picture of phase transitions, with examples taken from condensed matter physics. Emphasis is placed on notions of order, disorder, the role of correlation functions in critical phenomena, and the unifying concept of broken symmetry.

Students should be able to describe the generality of phase transitions and critical phenomena, distinguishing the key concepts of universality and broken symmetry with reference to variety of different phase transitions. They should be able to discuss the relevant experimental observations.

Students should be able to perform standard calculations for simple microscopic models which exhibit phase transitions, using the tools of equilibrium statistical mechanics. Central to this is the calculation of critical exponents at a continuous phase transition using mean field theory. They should know the basis for the Landau theory of phase transitions, the concept and significance of an order-parameter, and its connection with microscopic theories.

Students should be able to explain, with reference to GinzbUrg-Landau theory and numerical simulations, how spatial correlations become long-ranged at the critical point of a fluid or magnet, and how this motivates a scale-free description of the system. They should be able to explain, in qualitative terms, the idea of the renormalization group, and able to derive critical behavior for simple physical quantities from a scaling ansatz for the free energy.

The course will be taught by eighteen talk and chalk lectures, with guided reading in a variety of text books and several problem sheets. The notes on which the lectures are based will be published on Blackboard in advance of the lectures, and the problems set as exercises will be reviewed in three two-hour problems classes. Optional revision lectures will be provided in the run up to the final examination.

2-hour written exam (100%)

- J M Yeomans, Statistical Mechanics of Phase Transitions (Oxford University Press 1992)

- K Huang, Introduction to Statistical Physics (2nd Edition - Chapman & Hall 2009)

- M Plischke and B Bergersen, Equilibrium Statistical Physics (3rd edition - World Scientific 2006)