  We discuss the lattice formulation of the 't Hooft surface, that is, the
two-dimensional surface operator of a dual variable. The 't Hooft surface
describes the world sheets of topological vortices. We derive the formulas to
calculate the expectation value of the 't Hooft surface in the multiple-charge
lattice Abelian Higgs model and in the lattice non-Abelian Higgs model. As the
first demonstration of the formula, we compute the intervortex potential in the
charge-2 lattice Abelian Higgs model.
