  We investigate a model of closed $(d-1)$-dimensional soft-self-avoiding
random surfaces on a $d$-dimensional cubic lattice. The energy of a surface
configuration is given by $E=J(n_{2}+4k n_{4})$, where $n_{2}$ is the number of
edges, where two plaquettes meet at a right angle and $n_{4}$ is the number of
edges, where 4 plaquettes meet. This model can be represented as a
$\Z_{2}$-spin system with ferromagnetic nearest-neighbour-, antiferromagnetic
next-nearest-neighbour- and plaquette-interaction. It corresponds to a special
case of a general class of spin systems introduced by Wegner and Savvidy. Since
there is no term proportional to the surface area, the bare surface tension of
the model vanishes, in contrast to the ordinary Ising model. By a suitable
adaption of Peierls argument, we prove the existence of infinitely many ordered
low temperature phases for the case $k=0$. A low temperature expansion of the
free energy in 3 dimensions up to order $x^{38}$ ($x={e}^{-\beta J}$) shows,
that for $k>0$ only the ferromagnetic low temperature phases remain stable. An
analysis of low temperature expansions up to order $x^{44}$ for the
magnetization, susceptibility and specific heat in 3 dimensions yields critical
exponents, which are in agreement with previous results.
