Statistical Field Theory

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

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.

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.

​​T​he standard entry requirements comprise:

• 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)

You will be assessed via an examination and coursework. 

This is an on-campus module. Lectures will be held on a single day of the week, each week, during term time. You will be expected to be on-campus for these. Exact dates and times will be confirmed upon enrolment.

This module is offered as part of our flexible master’s awards in Professional Development. The awards are one of the most flexible currently offered in the UK, providing the opportunity to study a range of modules from across King’s, both on-campus and online. Whether you are looking for a promotion or to retrain, you have come to the right place.

Designed for mature professionals juggling life and work commitments, our postgraduate awards will enable you to study at your own pace. In challenging financial times, you are also able to fund your studies module-by-module. We will support you to select the right module diet that meets your objectives while ensuring that you are well prepared for success. We will also help you to build your professional network of peers from across our suite of CPD modules.

We can’t wait for you to continue your lifelong learning journey here at King’s.