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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2014/2015
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DRPS : Course Catalogue : School of Physics and Astronomy : Undergraduate (School of Physics and Astronomy)

Undergraduate Course: Advanced Statistical Physics (PHYS11007)

Course Outline
SchoolSchool of Physics and Astronomy CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Year 5 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryIn 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
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-requisitesNone
Course Delivery Information
Academic year 2014/15, 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 Physics2:00
Academic year 2014/15, 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)
Reading List
None
Additional Information
Graduate Attributes and Skills Not entered
KeywordsAdStP
Contacts
Course organiserProf Luigi Del Debbio
Tel: (0131 6)50 5212
Email: luigi.del.debbio@ed.ac.uk
Course secretaryMs Rebecca Thomas
Tel: (0131 6)50 7218
Email: R.Thomas@ed.ac.uk
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