A numerical study of the 3D random interchange and random loop models

Studied and implemented the simulation environment in C. Decreased by thousands of time the execution time compared to previous Matlab solution.

During my first summer as University student, I worked with Professor Daniel Ueltschi on the random interchange spin model, to develop a simulation environment and check whether the model provide the correct estimation for the 1/2 spin quantum Heisenberg ferromagnet.

This environment was modelled as a 4-dimensional lattice-like cube, which can be thought of as a 3-dimensional grid, with at each point an extra “time” dimension attached.

My work was specifically to write the environment from scratch, given that the current solution in R and Matlab could only work for cubes with side length of to 10 points in a reasonable time, whereas the model was only expected to be accurate when the space size was approximately infinite, which is definitely larger than 10!

Part of the research was also to find if we could find at what size the model was showing the correct characteristics, which we found to be of around 150. The environment was written from scratch in C, and the execution time was of the order of tenths of second for this size, which was a decrease by more than a thousands fold of the previous simulation program.

IOP publication: https://iopscience.iop.org/article/10.1088/1751-8113/48/34/345002
Arxiv: https://arxiv.org/abs/1505.00983