Undergraduate Course: Advanced Statistical Physics (PHYS11007)

Course Outline
School	School of Physics and Astronomy	College	College of Science and Engineering
Credit level (Normal year taken)	SCQF Level 11 (Year 5 Undergraduate)	Availability	Available to all students
SCQF Credits	10	ECTS Credits	5
Summary	In this course we will discuss equilibrium phase transition, of the first and second order, by using the Ising and the Gaussian models as examples. We will first review some basic concepts in statistical physics, then study critical phenomena. Phase transitions will be analysed first via mean field theory, then via the renormalisation group (RG), in real space. We will conclude with some discussion of the dynamics of the approach to equilibrium.
Course description	Part 1: General methods ż Fundamental aspects of statistical physics (revision) ż Ising model in 1D: exact solutions and correlations ż Gaussian model Part 2: Phase transitions ż Variational mean field, and mean field theory of phase transitions ż Landau theory of phase transitions ż Correlations in mean field and Landau theory Part 3: Scaling and the renormalisation group (RG) ż Scaling laws ż Decimation amd RG in 1 and 2 dimensions ż The RG flow ż RG in momentum space Part 4: Dynamics ż Random walk theory and the diffusion equation ż Langevin equation ż Fokker-Planck equation

Entry Requirements (not applicable to Visiting Students)
Pre-requisites		Co-requisites	It is RECOMMENDED that students also take Statistical Physics (PHYS11024)
Prohibited Combinations		Other requirements	At least 80 credit points accrued in courses of SCQF Level 9 or 10 drawn from Schedule Q.

Information for Visiting Students
Pre-requisites	None

Course Delivery Information

Academic year 2015/16, Available to all students (SV1)		Quota: None
Course Start	Semester 1
Timetable	Timetable
Learning and Teaching activities (Further Info)	Total Hours: 100 ( Lecture Hours 22, Supervised Practical/Workshop/Studio Hours 11, Summative Assessment Hours 2, Revision Session Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 61 )
Assessment (Further Info)	Written Exam 100 %, Coursework 0 %, Practical Exam 0 %
Additional Information (Assessment)	Degree Examination, 100% Visiting Student Variant Assessment Degree Examination, 100%
Feedback	Not entered
Exam Information
Exam Diet	Paper Name		Hours & Minutes
Main Exam Diet S2 (April/May)	Advanced Statistical Physics		2:00

Academic year 2015/16, Part-year visiting students only (VV1)		Quota: None
Course Start	Semester 1
Timetable	Timetable
Learning and Teaching activities (Further Info)	Total Hours: 100 ( Lecture Hours 22, Supervised Practical/Workshop/Studio Hours 11, Summative Assessment Hours 2, Revision Session Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 61 )
Assessment (Further Info)	Written Exam 100 %, Coursework 0 %, Practical Exam 0 %
Additional Information (Assessment)	Degree Examination, 100% Visiting Student Variant Assessment Degree Examination, 100%
Feedback	Not entered
Exam Information
Exam Diet	Paper Name		Hours & Minutes
Main Exam Diet S1 (December)	Advanced Statistical Physics (VV1)		2:00

Learning Outcomes
Upon successful completion of this course it is intended that a student will be able to: 1)Express expectation values in a canonical ensemble. 2)Discuss the phenomenology of first- and second-order phase transitions with particular reference to the Ising model and liquid-gas transition. 3)Understand what a critical exponent is and be able to derive scaling relations 4)Exactly solve the Ising and the Gaussian model in 1 spatial dimension 5)Calculate correlations in the Ising model 6)Understand what mean field theory is, how it can be used to analyse a phase transition 7)Discuss the validity of mean-field theory in terms of upper critical dimension and give an heuristic argument to suggest dc=4 8)Apply the RG transformation in 1 dimension (decimation) to an Ising-like system. 9)State the RG transformation and discuss the nature of its fixed points for a symmetry-breaking phase transformation 10)Study the fixed points of an RG flow and understand their physical meaning 11)Understand what the Langevin and the Fokker-Planck equations are and how they can be related. 12)Be able to compute expectations of random variables with the Langevin equation, and to solve the Langevin and Fokker-Planck equations in simple cases (1 dimension)