  We have devised an isotropic interaction potential that gives rise to
negative thermal expansion (NTE) behavior in equilibrium many-particle systems
in both two and three dimensions over a wide temperature and pressure range
(including zero pressure). An optimization procedure is used in order to find a
potential that yields a strong NTE effect. A key feature of the potential that
gives rise to this behavior is the softened interior of its basin of
attraction. Although such anomalous behavior is well known in material systems
with directional interactions (e.g., zirconium tungstate), to our knowledge
this is the first time that NTE behavior has been established to occur in
single-component many-particle systems for isotropic interactions. Using
constant-pressure Monte Carlo simulations, we show that as the temperature is
increased, the system exhibits negative, zero and then positive thermal
expansion before melting (for both two- and three-dimensional systems). The
behavior is explicitly compared to that of a Lennard-Jones system, which
exhibits typical expansion upon heating for all temperatures and pressures.
