Proceedings of the 2025-2026 COMPASS Final Project

This volume presents five computational-physics studies produced during the COMPASS 2025 program. The first three tackle the gravitational N-body problem, exploring how the Barnes-Hut tree algorithm and the Particle-Mesh FFT method can replace brute-force pairwise summation to simulate systems of up to 500 bodies with collision-driven shockwaves at a fraction of the computational cost. The remaining two studies investigate the 2D Ising model, benchmarking local-update algorithms (Metropolis and Heat Bath) against cluster methods (Wolff and Swendsen-Wang) to understand how critical slowing down near the phase transition can be overcome. Across all five papers, the authors learned first-hand how to balance accuracy against efficiency, choose the right algorithm for a given physical regime, and diagnose numerical artifacts through energy conservation, autocorrelation analysis, and trajectory tracking.