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: Ising and Landau Ginzburg Mean Field -Revision -1D Ising model: Transfer matrix and correlations -Landau theory -Spinodal decomposition -Variational mean field theory -Correlations in Landau-Ginzburg theory, and the Ginzburg criterion -Complex Landau-Ginzburg theory Part 2: Renormalisation Group (RG) -Widom¿s scaling ansatz and scaling laws -Renormalisation group theory -Theory of rescaling and decimation -RG flow -2D RG Part 3: Field Dynamics -Non-conserved dynamics (model A) -Conserved dynamics (model B) -Noisy dynamics: Random walks and the generalized 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-requisites	None
High Demand Course?	Yes

Course Delivery Information

Academic year 2021/22, 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 2021/22, 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
No Exam Information

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)Know what Model A and B are and how they can be used to study the dynamics of fields to equilibrium. 12)Understand what the Langevin and the Fokker-Planck equations are and how they can be related. 13)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
Keywords	AdStP

Contacts
Course organiser	Mr Davide Michieletto Tel: Email: Davide.Michieletto@ed.ac.uk	Course secretary	Miss Stephanie Blakey Tel: (0131 6)68 8261 Email: steph.blakey@ed.ac.uk