Abstract
Spacelike-Wilson-loop operator averages are considered quantitatively in Hamiltonian lattice gauge theory. In 2 + 1 dimensions it is argued that no roughening transition is expected, that is, the spanning surface of an infinite-area loop is always rough, and so a good signal of the deconfining bulk transition should be obtained from strong-coupling expansions. It is shown that the surface width diverges, and that the roughening-induced $\frac{1}{R}$ potential has the expected strength. Generalizations are discussed and problems pointed out.
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