Nobel prize-winning physicist who challenged accepted thinking in key areas

David Thouless, who has died aged 84, won half of the 2016 Nobel prize in physics, the other half being shared by Duncan Haldane and me. David and I solved an interesting theoretical problem by introducing some new ideas with important implications, and so unknowingly created a new field in the discipline.

Our main innovation came from topology: the mathematical study of the properties preserved when objects are twisted, stretched or crumpled, properties that change only step by step. From 1972 to 1974 we sought a theoretical explanation of a phase transition, a change of state such as water turning into steam and back to water again, from a high-temperature disordered phase, a gas, to a low-temperature partially ordered one, a liquid such as water, in an arrangement operating in two dimensions – a thin film or layer of something not supported by anything else. Previously it had been thought for very good reasons that such a phase transition could not happen in two dimensions, but only in three or more.

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