Lennard-Jones Molecular Dynamics

300 disks in a periodic box interacting through the Lennard-Jones potential $U(r)=4\varepsilon[(\sigma/r)^{12}-(\sigma/r)^{6}]$ (reduced units $\sigma=\varepsilon=m=k_B=1$), integrated by velocity-Verlet (the verified shared symplectic engine) with a shifted-force cutoff so energy is conserved. Particles are coloured by kinetic energy. The temperature is read from the kinetic energy by equipartition, the pressure from the virial, and the structure from the radial distribution $g(r)$: a flat $g(r)\to1$ for a gas, a strong first peak near $r=2^{1/6}\sigma$ for a dense liquid. Set it cold and dense and it freezes into a triangular lattice; heat it and it melts.