  We formulate a new geometrical string on the euclidean lattice. It is
possible to find such spin systems with local interaction which reproduce the
same surface dynamics.In the three-dimensional case this spin system is a usual
Ising ferromagnet with additional diagonal antiferromagnetic interaction and
with specially adjusted coupling constants. In the four-dimensional case the
spin system coincides with the gauge Ising system with an additional
double-plaquette interaction and also with specially tuned coupling constants.
We extend this construction to random walks and random hypersurfaces (membrane
and p-branes) of high dimensionality. We compare these spin systems with the
eight-vertex model and BNNNI models.
