Monte Carlo (MC) and Molecular Dynamics (MD) simulations are powerful
tools for understanding the low temperature properties of systems of i
nteracting electrons and phonons in a solid, including the phenomena o
f magnetism and superconductivity. When mobile electrons are studied,
these simulations are currently limited to a few hundred particles, an
d also largely to ''clean'' systems where no defects are present. Ther
efore, more powerful machines and algorithms must be used to address m
any of the most important issues in the field. In this paper, we prese
nt results from using some simple implementations of the p4 parallel p
rogramming system on a variety of parallel architectures to conduct MC
and MD simulations of one and two dimensional electron-phonon models.