Advanced Statistical Physics (U01426)

? Credit Points : 10 ? SCQF Level : 11 ? Acronym : PHY-5-AdvStatPh

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.

Entry Requirements

? Pre-requisites : At least 80 credit points accrued in courses of SCQF Level 9 or 10 drawn from Schedule Q. Prior/concurrent attendance at Statistical Physics (PHY-4-StatPh) is desirable.

Variants

? This course has variants for part year visiting students, as follows

Advanced Statistical Physics (VS1) (Semester 1 (Blocks 1-2))

Subject Areas

Home subject area

Undergraduate (School of Physics), (School of Physics, Schedule Q)

Delivery Information

? Normal year taken : 5th year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
18/09/2007	11:00	12:00	Lecture Room 3218, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Tuesday	11:10	12:00	KB
Lecture	Friday	11:10	12:00	KB

Summary of Intended 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)