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
¿ Fundamental aspects of statistical physics (revision)
¿ Ising model in 1D: exact solutions and correlations
¿ Gaussian model
Part 2: Phase transitions
¿ Variational mean field, and mean field theory of phase transitions
¿ Landau theory of phase transitions
¿ Correlations in mean field and Landau theory
Part 3: Scaling and the renormalisation group (RG)
¿ Scaling laws
¿ Decimation amd RG in 1 and 2 dimensions
¿ The RG flow
¿ RG in momentum space
Part 4: Dynamics
¿ Random walk theory and the diffusion equation
¿ Langevin equation
¿ FokkerPlanck equation

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  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
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2019/20, 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)   2:00  

Academic year 2019/20, Partyear 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)  Semester 1 Visiting Students Only  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 secondorder phase transitions with particular reference to the Ising model and liquidgas 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 meanfield 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 Isinglike system.
9)State the RG transformation and discuss the nature of its fixed points for a symmetrybreaking phase transformation
10)Study the fixed points of an RG flow and understand their physical meaning
11)Understand what the Langevin and the FokkerPlanck 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 FokkerPlanck equations in simple cases (1 dimension)

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  AdStP 
Contacts
Course organiser  Prof Martin Evans
Tel: (0131 6)50 5294
Email: M.Evans@ed.ac.uk 
Course secretary  Mrs Alicja Ross
Tel: (0131 6)51 3448
Email: Ala.Ross@ed.ac.uk 

