British-born researchers David J Thouless, F Duncan M Haldane and J Michael Kosterlitz on Tuesday won the 2016 Nobel Prize in Physics for groundbreaking discoveries on matter.
The Royal Swedish Academy of Sciences cited them for "theoretical discoveries of topological phase transitions and topological phases of matter."
Topology is a branch of mathematics that describes the properties that remain intact when an object is stretched, twisted or deformed, but not if it is torn apart.
"This year's laureates opened the door on an unknown world where matter can assume strange states," the academy said in a statement.
The winners used advanced mathematical methods to study unusual phases of matter, including superconductors, superfluids or thin magnetic films, the academy said.
"Thanks to their pioneering work ... many people are hopeful of future applications in both materials science and electronics," the statement added.
Kosterlitz and Thouless have studied phenomena that arise in a flat world - on surfaces or inside extremely thin layers that can be considered two-dimensional - while Haldane also studied matter that forms threads so thin they can be considered one-dimensional, the academy said.
Researchers long believed that in a flat, two-dimensional world, thermal fluctuations destroy all order in matter, even at absolute zero.
But in the early 1970s, Thouless and Kosterlitz met in the British city of Birmingham and developed an entirely new understanding of phase transitions called the KT transition, which is regarded as one of the 20th century's most important discoveries in the theory of condensed matter physics, the academy said.
In the 1980s, both Thouless and Haldane presented groundbreaking new theoretical work that challenged previous theories, of which one was the quantum mechanical theory for determining which materials conduct electricity.
Haldane, a British-born researcher and physics professor at Princeton University in the US state of New Jersey, said he was "very, very surprised and very gratified" to win the award.
"Like most discoveries you stumble onto them," Haldane said, speaking by phone to reporters at the Royal Swedish Academy of Sciences.
"One never realizes the full implications of these things," he added.
On his research, he recalled how during the 1980s he "didn't think it would ever find a practical realization."
Co-laureate Kosterlitz of Brown University in the US state of Rhode Island, said he was "more than slightly surprised."
Kosterlitz told Swedish Radio's science desk he was visiting a colleague in Espoo, Finland when he learned of the win. He had not expected the award as the work had been done "a long time ago."
He planned to celebrate with a few beers, he said.
Kosterlitz was born 1942 in Aberdeen, Scotland.
Haldane and Kosterlitz share one half of the prize worth 8 million kronor (930,000 dollars). The other half goes to Thouless, born 1934 in Bearsden, Scotland, an emeritus professor at the US University of Washington in Seattle, Washington.
The physics prize is the second of the 2016 Nobel Prize awards to be announced. The medicine prize was awarded to Japanese scientist Yoshinori Ohsumi on Monday. The awards were endowed by Swedish industrialist Alfred Nobel, inventor of dynamite.