Crystal Ball: A Simple Model for Phase Transitions on a Classical Spherical Lattice

When compressed, certain lattices undergo phase transitions that may allow nuclei to gain significant kinetic energy. To explore the dynamics of this phenomenon, we develop a framework to study Coulomb coupled N-body systems constrained to a parametric surface, focusing specifically on the case of a sphere, as in the Thomson problem. We initialize $N$ total Boron nuclei as point particles on the surface of a sphere, allowing the particles to equilibrate via Coulomb scattering with a viscous damping term. To simulate a phase transition, we remove $N_{rm}$ particles, forcing the system to rearrange into a new equilibrium. We develop a scaling relation for the average peak kinetic energy attained by a single particle as a function of $N$ and $N_{rm}$. For certain values of $N$, we find an order of magnitude energy gain when increasing $N_{rm}$ from 1 to 6, indicating that it may be possible to engineer a lattice that maximizes the energy output.