  We study the Polyakov loop correlator in the (2+1) dimensional Z_2 gauge
model. An algorithm that we have presented recently, allows us to reach high
precision results for a large range of distances and temperatures, giving us
the opportunity to test predictions of the effective Nambu-Goto string model.
Here we focus on the regime of low temperatures and small distances. In
contrast to the high temperature, large distance regime, we find that our
numerical results are not well described by the two loop-prediction of the
Nambu-Goto model. In addition we compare our data with those for the SU(2) and
SU(3) gauge models in (2+1) dimensions obtained by other authors. We generalize
the result of L\"uscher and Weisz for a boundary term in the interquark
potential to the finite temperature case.
