Computer simulation of phase transitions in classical and quantum systems

The melting transition of classical hard disks is reviewed, emphasizing evidence from computer simulation for the order of the transition, mechanism of melting, and convergence of the virial expansion. Next, the graph theoretical treatment of a dilute mixture of electrolytes consisting of stripped iron ions in a hydrogen plasma is examined for fluid phase separation at the center of the sun. For quantum many‐body systems a stochastic numerical scheme is outlined and applied to the Fermi electron gas at 0 K to locate the melting transition and the region of stability of the ferromagnetic fluid phase. Finite temperature results for the electron gas are used to estimate the region of convergence of the expansion away from the classical limit. Results for the superfluid transition of helium are compared to those of the ideal gas. Preliminary results leading to a prediction for the molecular to metal transition in hydrogen are also presented.