  Reaching a ground state of a spin system is analogous to a protein evolving
into its native state. We study the ``folding'' times for various random Ising
spin systems and determine characteristic temperatures that relate to the
``folding''. Under optimal kinetic conditions, the ``folding'' times scale with
the system size as a power law with a non-universal exponent. This is similar
to what happens in model proteins. On the other hand, the scaling behavior of
the characteristic temperatures is different than in model proteins. Both in
the spin systems and in proteins, the folding properties deteriorate with the
system size.
