  Statistical mechanical models with local interactions in $d>1$ dimension can
be regarded as $d=1$ dimensional models with regular long range interactions.
In this paper we study the critical properties of Ising models having $V$
sites, each having $z$ randomly chosen neighbors. For $z=2$ the model reduces
to the $d=1$ Ising model. For $z= \infty$ we get a mean field model. We find
that for finite $z > 2$ the system has a second order phase transition
characterized by a length scale $L={\rm ln}V$ and mean field critical exponents
that are independent of $z$.
