Samuel Frederick Edwards

Samuel Frederick Edwards, a leader in several fields of physics, died peacefully on 7 May 2015 in Cambridge, UK.

Born in Swansea, Wales, on 1 February 1928, Edwards studied at Cambridge University and earned his degree in mathematics in 1949. He joined Julian Schwinger at Harvard University and received his PhD on the structure of the electron in 1951. There he adopted the functional methods that he later used to transform many areas of physics and establish yet others.

After a year at Princeton University, Edwards returned to the UK and joined the Birmingham group of Rudolf Peierls. He then went to the University of Manchester, where he was a professor of theoretical physics and worked on turbulence, statistical mechanics, and quantum many-body theory of transport in metals.

An isolated polymer chain is a formidable, non-Markov problem—it is a self-avoiding, spatial random walk. Edwards used field theory to calculate Paul Flory’s celebrated $\raisebox{1ex}{$6$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$ scaling exponent for chain extent. He was quick to recognize the universality of that and similar problems in which detailed molecular structure is irrelevant. He then showed that dense solutions and melts of chains are less difficult problems, just as metallic electrons are essentially free, with an effective mass subsuming all detail.

Edwards attacked the problems of chain dynamics and of cross-linked networks (rubber). He also saw that entanglement constraints effectively create a confining tube. Pierre-Gilles de Gennes then extended that concept to molten chains that can crawl, or “reptate,” along the tube. So began a lifelong friendship and gentle rivalry between Edwards and de Gennes, who visited the Cambridge group often. His visits were an admirable excuse for the fabulous dinners Edwards hosted at the college and for more intimate dinners at home.

As Edwards observed, polymer networks contain locally mobile chains but with quenched connectivity and topology that create a solid from a liquid. Computing their free energy required averaging the logarithm of the partition function over quenched variables. Edwards solved that deep technical challenge by returning to field theory, this time with n components, each describing a different replica of the same system. Simple averaging over all variables and letting n tend to zero was equivalent to averaging the logarithm. Edwards’s replica trick made both network and tube constraints tractable. Edwards, with collaborators, also used it to good effect in the random matrix problem and its generalizations.

In the early 1970s, Edwards was back in Cambridge, in the Cavendish theory group, alongside Philip Anderson. Together they applied the replica trick to the spin-glass problem, in which magnetic spins interact with each other via fixed random couplings. Their celebrated papers launched a field that took decades to reach maturity and remains active today. Edwards once said, “I may not have had the last word on that subject, but at least I had the first word.” Considerable theory worldwide was directed toward more formal aspects of replica theory. Spin-glass theory now underpins simulated annealing, machine learning, fuzzy logic, and neural networks, all much exploited in our information age.

Edwards was head of the UK’s Science Research Council from 1973 to 1977. His daily commute from Cambridge to London gave him time to carry out seminal work: Alongside spin glasses, he extended network and polymer dynamics to include the nonlinear effects of entanglements.

His groundbreaking work with Masao Doi, then a postdoc from Tokyo, would have a profound effect on a problem of huge industrial importance: high-polymer-melt rheology. When a polymer melt is sheared, chains respond elastically as if in rubber until they have had time to reptate out of their confining tube. Stress has then relaxed. The supreme achievement of the Doi–Edwards theory was to describe in detail such nonlinear viscoelasticity, which pervades all long-chain polymer response and all processing of molten plastics. A huge community of theoretical, experimental, and industrial researchers and technologists subsequently tested, extended, and applied those theories. In both the polymer and spin-glass communities, Edwards’s work had an electrifying effect.

On returning full-time to Cambridge, Edwards’s contact with industry grew because of his governmental experience, his judgment, and the extreme importance of his discoveries to the chemical and food industries. He gave industry invaluable guidance, and industry in return gave substantial support to academic research at Cambridge.

In 1984 Edwards became the eighth Cavendish Professor, a worthy successor to James Clerk Maxwell, Lord Rayleigh, J. J. Thomson, Ernest Rutherford, William Bragg, Nevill Mott, and Brian Pippard. He continued founding new fields and turning powerful methods to established fields not yet studied by physicists. For instance, with a colleague working in theoretical physics, he extended the scaling laws for the mechanical properties of dry, solid foams to cellular solids modified by filling liquids. Fluid flow, elasticity, and fluid-induced failure are coupled. Those models are used by industry for many foodstuffs. Another field—granular matter—preoccupied Edwards into old age. For granular materials, the equivalent to inverse temperature, in the statistical mechanical sense, is now called the Edwards compactivity. In his later years, he would bicycle so deep in thought and so slowly that colleagues would observe, “Here is Sam making an adiabatic transition from home to the lab!”

Edwards had a deep interest in music: Before his 70th birthday celebrations, de Gennes proposed that Edwards be offered a ride in a hot-air balloon, a gift he declined in favor of the complete works of Bach on CD! His knowledge of and generosity with fine wines were a pleasure shared with friends.

Edwards is remembered fondly for his insights, generosity with his wisdom, and his mercurial intellect.