He is best known for his work in theoretical condensed matter physics and statistical mechanics, and in particular for research on critical phenomena and two-dimensional conformal field theory.
He was an undergraduate and postgraduate student (now an Honorary Fellow) at Downing College, Cambridge, before moving to the University of California, Santa Barbara, where he joined the faculty in 1977.
After this, he applied methods of quantum field theory and the renormalization group to condensed matter, especially to critical phenomena in both pure and disordered equilibrium and non-equilibrium systems.
This helped inspire the work of mathematicians which was recognised by the award of the Fields Medal to Wendelin Werner in 2006, and to Stanislav Smirnov in 2010.
More recently he has worked on questions of quantum entanglement and non-equilibrium dynamics in many-body systems, and on non-local field theory.