  We exactly rewrite the Z(2) lattice gauge theory with standard plaquette
action as a random surface model equivalent to the untruncated set of its
strong coupling graphs. By extending the worm approach applied to spin models
we simulate such surfaces including Polyakov line defects that randomly walk
over the lattice. Our Monte Carlo algorithms for the graph ensemble are
reasonably efficient but not free of critical slowing down. Polyakov line
correlators can be measured in this approach with small relative errors that
are independent of the separation. As a first application our results are
confronted with effective string theory predictions. In addition, the excess
free energy due to twisted boundary conditions becomes an easily accessible
observable. Our numerical experiments are in three dimensions, but the method
is expected to work in any dimension.
