  We study spin models underlying the non-planar dynamics of ${\cal N}=4$ SYM
gauge theory. In particular, we derive the non-local spin chain Hamiltonian
generating dilatations in the gauge theory at leading order in $g_{\rm YM}^2 N$
but exact in ${1\over N}$.
  States in the spin chain are characterized by a spin-configuration and a
linking variable describing how sites in the chain are connected. Joining and
splitting of string/traces are mimicked by a twist operator acting on the
linking variable. The results are applied to a systematic study of non-planar
anomalous dimensions and operator mixing in ${\cal N}=4$ SYM. Intriguingly, we
identify a sequence of SYM operators for which corrections to the one-loop
anomalous dimensions stop at the first ${1\over N}$ non-planar order.
