Duminil-Copin and Smirnov used percolation theory and the vertices and edges connecting them in a lattice to model fluid flow and with it phase transitions.

The pair investigated the number of self-avoiding walks that were possible in hexagonal lattices, connecting combinatorics to percolation theory.

[4] Since 2017, Duminil-Copin has been the principal investigator of the European Research Council – Starting Grant “Critical behavior of lattice models (CriBLam)”.

In collaboration with Vincent Beffara in 2011, he was able to produce a formula for a determining the critical point for many two-dimensional dependent percolation models.

[1] In 2019, along with Vincent Tassion and Aran Raoufi, he published research on the size of connected components in the lattice when the system is just below and above the critical point.

Duminil-Copin and his associates proved this characteristic, which they called "sharpness", using mathematical analysis and computer science.

[7] Duminil-Copin was awarded the Fields Medal in 2022 for "solving longstanding problems in the probabilistic theory of phase transitions in statistical physics, especially in dimensions three and four".