Sandpiles and avalanches: the work that won Deepak Dhar the Dirac Medal

The theoretical physicist Deepak Dhar has been awarded the Dirac Medal for his contributions to statistical physics, sharing the honour with Bernard Derrida, Marc Mezard and Haim Sompolinsky. He is only the second scientist based in India to receive it, after the string theorist Ashoke Sen in 2012, and he has spent most of his career in India.

Dhar is known in physics circles for his work on Abelian sandpiles. The idea begins with a simple picture. Drop grains of sand one at a time onto a flat surface. The pile grows until it becomes steep enough that a new grain shifts it, sometimes causing a modest slide and sometimes an avalanche. Which grain triggers which size of event is very hard to predict in advance.

In the late 1980s the physicists Per Bak, Chao Tang and Kurt Wiesenfeld proposed that this behaviour might be a general principle underlying many natural phenomena, from earthquakes to forest fires to the extinction of species. They called it self-organised criticality, meaning a system that organises itself into a delicately balanced state where even a small nudge can produce an effect of any size.

Dhar and his collaborators turned that picture into mathematics with the Abelian sandpile model. The word Abelian carries the key insight: no matter what sequence the grains topple and cascade in, the pile always settles into the same final shape. That property is what allows physicists to calculate exact answers and predict the outcome, rather than only simulating it.

The model has found wide application precisely because it captures something general, namely systems that build up instability until they release it unpredictably. Scientists have used it to model earthquakes, the spread of forest fires, bursts of activity in the brain's neural networks, and fluctuations in financial markets.

Dhar was born in 1951 in Pratapgarh, Uttar Pradesh. He studied at Allahabad University, took his master's degree at IIT Kanpur, and completed his PhD at the California Institute of Technology in 1978, where he was a teaching assistant to Richard Feynman. He then returned to India rather than remain in the United States, spending most of his career at the Tata Institute of Fundamental Research in Mumbai before moving to IISER Pune in 2016. Since 2024 he has been INSA Distinguished Professor at the International Centre for Theoretical Sciences in Bengaluru. His earlier honours include the Shanti Swarup Bhatnagar Prize in 1991, the TWAS Prize in 2002, the Boltzmann Medal in 2022 and the Padma Bhushan in 2023.

The Dirac Medal itself was established in 1985 by the International Centre for Theoretical Physics in Trieste, and is announced each year on the birthday of Paul Dirac, whose equations helped lay the foundations of quantum mechanics. It goes to physicists who have made outstanding contributions but have not already received the very top honours, and is explicitly not awarded to Nobel laureates, Fields Medallists or Wolf Prize laureates. Past recipients include Edward Witten, Stephen Hawking and Leonard Susskind, and several have gone on to win a Nobel Prize. The ICTP was founded in 1964 by the Pakistani physicist and Nobel laureate Abdus Salam with the Italian government and the International Atomic Energy Agency, as a place where physicists from the Global South could work alongside colleagues from around the world.