Research Highlights

Context

The Ising model was created nearly 100 years ago as a universal model to study phase transitions and the formation of patterns during such events. Hugo Duminil-Copin won 2022 Fields Medal for proving that phase transitions exist only in the dimensions of 2, 3 and 4.

The Science

Each particle has a fixed number of "neighbors". Changing one particle implies changing its interation with all neighbors, which recursively impacts 2nd degree neighbors (this is also a reason this topic is intrigueingly computational). Higher dimension typically implies larger number of neighbors; however, it is possible to pack more neighbors in a lower dimension.

In the above 2-D figure, each particle has 6 neighbors, same as in 3-D where each particle can be seen as a cube with 6 faces and thus 6 neighbors. The number of neighbors is the same, but simulations in this study show that phase transitions happen at a lower temperature in the 2-D figure.

Engineering

The lattice has been divided into a grid system, to allow for multi-thread computations.

The code reindexes any point on the grid into each thread's proprietory memory if it is in the blue region, any point into shared memory if it is in the red region.

The Reason I'm in this

I chose this project to keep abreast of the latest developments in probability theory especially given I have worked on a couple other related areas. The software package is one of the few open-source packages that produce cluster formations in the 3 dimensinonal space.