From his obituary in the NY Times:

Kenneth G. Wilson, who was awarded the 1982 Nobel Prize in Physics for showing how to calculate tricky moments like when ice melts or an iron bar loses its magnetism, died on Saturday in Saco, Me. He was 77…

From the start, Dr. Wilson was drawn to difficult problems that could take years to solve, said Kurt Gottfried, a Cornell colleague. One such problem was phase transitions, the passage from water to steam or atoms lining up to make a magnet. At the critical point — the temperature at which the change happens — orderly behavior breaks down, but theorists had few clues to how to calculate what was happening.

Dr. Wilson realized that the key to the problem was that fluctuations were happening on all scales at once — from the jostling and zooming of individual atoms to the oscillations of the entire system — something conventional theory could not handle.

At the heart of Dr. Wilson’s work was an abstruse mathematical apparatus known as the renormalization group, which had been conceived by his thesis adviser, Dr. Gell-Mann, and Francis Low in 1951. They had pointed out that fundamental properties of particles and forces varied depending on the scale over which they are measured.

Dr. Wilson realized that such “scaling” was intrinsic to the problems in phase transitions. In a series of papers in the early 1970s, building on the work of Michael Fisher and Benjamin Widom at Cornell and Leo Kadanoff, then at the University of Illinois, he applied the renormalization idea to show how the critical phenomena could be solved by dividing the problem up into simpler pieces, so that what was happening at the melting point, for example, could be considered on one scale at a time.

The results showed that many seemingly unrelated systems — from magnets to liquids — could exhibit the same characteristic behavior as they approached the critical point. The concept proved to be of wide relevance in physics and was cited by the Royal Swedish Academy of Sciences in presenting the Nobel.

I can’t claim to know his work in detail but, even though my grad work was in a very different field, I was aware of it and appreciated it’s significance.  (It was a lecture by Ben Widom – whose work is noted in Wilson’s obit – which got me interested in physical chemistry and started me down the path to doing what I do now.)