Unit information: The Physics of Phase Transitions. in 2020/21

Unit name	The Physics of Phase Transitions.
Unit code	PHYSM0300
Credit points	10
Level of study	M/7
Teaching block(s)	Teaching Block 2 (weeks 13 - 24)
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

Description including Unit Aims

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.

Intended Learning Outcomes

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.

Teaching Information

The unit will be taught through a combination of

• asynchronous online materials, including narrated presentations and worked examples
• synchronous group problems classes, workshops, tutorials and/or office hours
• asynchronous directed individual formative exercises and other exercises
• guided, structured reading

Assessment Information

Written timed, open-book examination (100%)

Reading and References

• 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)