My research interest is in Model Magnets -- real magnetic systems that approximate idealised models of many-body behaviour. In the early part of my career I made three significant discoveries:
* In 1993, along with Peter Holdsworth (Lyon) I used renormalization group methods to calculate a universal and frequently observed critical exponent for magnetic films and other two-dimensional systems (beta = 0.23). This today stands as a textbook result in low dimensional magnetism.
* In 1997, along with Mark Harris (Edinburgh) I invented the concept of "spin ice", named it, and discovered its experimental realisations among magnetic oxides of the pyrochlore family. Spin ice is a magnet state that defies the Third Law of thermodynamics and supports magnetic monopole excitations. We named on account of its close analogy with the statistical physics of water ice. By 2019 spin ice has been referred to more than 5000 times in the scientific literature.
* In 1998, with Peter Holdsworth and Jean-François Pinton (Lyon) I established an analogy between magnetic critical behavior and turbulent flow that led to a probability distribution being named after us - the Bramwell-Holdsworth-Pinton (BHP) distribution. This result has stimulated much research into non-equlibrium fluctuations in turbulence, geophysics, astrophysics and beyond.
More recently I have worked on general critical exponents in two dimensional systems, on magnetic monopoles in spin ice, on magnetic Coulomb phases, on spin ice thin films, on emergent electrochemistry in magnetism, on demagnetizing factors, on water ice and on measurement of the quantum adiabatic susceptibility. .