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.
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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
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Entry Requirements (not applicable to Visiting Students)
Pre-requisites |
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Co-requisites | It is RECOMMENDED that students also take
Statistical Physics (PHYS11024)
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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 |
High Demand Course? |
Yes |
Course Delivery Information
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Academic year 2020/21, Available to all students (SV1)
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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 )
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Assessment (Further Info) |
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %
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Additional Information (Assessment) |
Degree Examination, 100%
Visiting Student Variant Assessment
Degree Examination, 100% |
Feedback |
Not entered |
Exam Information |
Exam Diet |
Paper Name |
Hours & Minutes |
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Main Exam Diet S2 (April/May) | | 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)
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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 | Miss Stephanie Blakey
Tel: (0131 6)68 8261
Email: steph.blakey@ed.ac.uk |
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