From the P * P correlator one can extract the static quark-antiquark potential V (r) by V (r) = − 1 T ln P * P(r) . We prefer to look at the first and the second derivative of this potential for the force between the quark and the antiquark and information about sub-leading terms. To facilitate our comparison with string models we actually compute a scaled second derivative which we call c(r). This quantity is expected to become the Lüscher term (= − (d−2)π 24 ) asymptotically. On the lattice these are given by
F(r) = V (r) −V (r − 1) & c(r) =r 3 2 [V (r + 1) +V (r − 1) − 2V (r)] (3.1) wherer = r + a 2 + O(a 2 ) andr = r + O(a 2 )
are defined as in [9] to reduce lattice artifacts. For large distances, we are going to concentrate on the potential due to the NG string, the so called Arvis potential [16] given by V Arvis 
= σ r 1 − (d−2)π 12σ r 2 1/2
. We will define the L.O. and N.L.O. approximations by retaining 1/r and 1/r 3 terms in the potential respectively. We will compare our lattice **data** on force and c(r) with predictions from leading order, NLO and from the full Arvis potential.