Short distance behaviour of the effective string

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 Lüscher and Weisz for a boundary term in the interquark potential to the finite temperature case