Statistical Field Theory

Topics may include:

• Overview 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
• MSR formalism, related to Fokker-Planck formalism. Discussion of simple cases of Brownian walker and population dynamics using both tools
• Notion of detailed-balance
• How renormalisation can be usefully applied within MSR formalism (e.g. examples of reaction-diffusion systems).

This module applies the methods of quantum field theory (QFT) and renormalisation group to problems in quantum and classical many-body physics. The module will introduce you to profound ideas such as universality, and the use of Wilsonian renormalisation methods to provide quantitative predictions for the behaviours of both classical and quantum many-body systems (including magnets and superfluids). These methods form the basis of our modern understanding of the notion of ‘phase of matter’, and the module will touch on wider applications in the study of high-energy physics, and non-equilibrium phenomena.

By the end of the module, you will be able to:

• Formulate many-body statistical mechanics in terms of functional integrals
• 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. ϕ4)
• Formulate stochastic differential equations using the Martin-Siggia-Rose (MSR) field theory formalism
• 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).

You will be assessed via an examination. 

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.