  This work is dedicated to the study of a supersymmetric quantum spherical
spin system with short-range interactions. We examine the critical properties
both a zero and finite temperature. The model undergoes a quantum phase
transition at zero temperature without breaking supersymmetry. At finite
temperature the supersymmetry is broken and the system exhibits a thermal phase
transition. We determine the critical dimensions and compute critical
exponents. In particular, we find that the model is characterized by a
dynamical critical exponent $z=2$. We also investigate properties of
correlations in the one-dimensional lattice. Finally, we explore the connection
with a nonrelativistic version of the supersymmetric $O(N)$ nonlinear sigma
model and show that it is equivalent to the system of spherical spins in the
large $N$ limit.
