Program start date | Application deadline |
2026-01-19 | - |
Program Overview
Statistical Field Theory (7CCP5000M)
Course Overview
Besides the solid-liquid-gas trinity of states, quantum matter can realise a cornucopia of phases, such as magnetic states, electronically ordered states, and quantum condensates. This course presents the modern understanding of “phases of matter” and the transitions between them. We will develop and apply concepts and methodologies from statistical / quantum field theory (S/QFT) in the context of many-body physics. The first part of the module will be centred around the “correlated electron problem” and phase transitions in condensed matter (such as metal-insulator, non-magnetic to magnetic, and normal-state to superconducting transitions), introducing, among others, the notion of spontaneous symmetry breaking and the emergence of associated collective (Goldstone) excitations. The more general, second part will formalise critical phenomena and discuss ideas such as universality (why, near criticality, the same description applies to a wide range of systems), introduce aspects of the renormalization group approach, and develop and apply Ginzburg-Landau theory and beyond.
Course Details
- Duration: 11 weeks
- Credit level: 7
- Credit value: 15
- Fees:
- Full Price: £1,125.00
- International: £3,150.00
Entry Requirements
- A 2:2 honours degree or international equivalent in Physics: Statistical mechanics, quantum mechanics plus condensed matter
- A CV and personal statement outlining your reasons for study
- English language band D (for example, IELTS 6.5 overall with a minimum of 6.0 in each skill)
- Recommended: Modelling Quantum Many-body Systems (7CCPNE05; 1st semester)
Assessment
- Examination
- Coursework
Learning Outcomes
By the end of the module, you will be able to:
- Understand and apply techniques to interacting quantum many-body systems at finite temperatures (Green’s functions/Feynman diagrams)
- Formulate many-body statistical mechanics in terms of functional integrals and second quantization
- Apply a systematic understanding of mean-field theory, upper- and lower-critical dimension to relevant systems
- Identify and demonstrate the idea of universality, i.e. why the same mathematical theories describe a wide range of physical systems
- Perform the simplest Wilsonian renormalisation group calculations (e.g. blockspin or ϕ4)
- Identify and apply the most relevant tools introduced in the module to unfamiliar systems, analysing the potential and limitations of such tools.
Course Features
Topics may include:
- Overview of phase transitions in interacting quantum many-body systems (metal-insulator transition, magnetism, superconductivity)
- Spontaneous symmetry breaking and associated collective (Goldstone) modes
- Classification of phase transitions, the notion of critical exponent, and the experimental evidence for universality
- Ising ferromagnet, and its description in terms of ϕ4-theory
- Mean-field theory for ϕ4-theory. Landau-criterion. Upper and lower critical dimensions
- Idea of renormalisation. Block-spin renormalisation in 1D, and the absence of a transition
- The notion of relevant and irrelevant operators
- Perturbative Wilsonian renormalisation group in d = 4 − epsilon dimensions for ϕ4-theory. Predictions for critical exponents
Delivery
- Delivery mode: In person
- Places: Course closed
- Application deadline: 01 December 2025
- Dates: 19 January 2026 - 01 May 2026
Faculty
- Offered by: Faculty of Natural, Mathematical & Engineering Sciences
- Department: Department of Physics