A statistical model of loops on the three-dimensional lattice is proposed and
is investigated. It is O(n)-type but has loop fugacity that depends on global
three-dimensional shapes of loops in a particular fashion. It is shown that,
despite this non-locality and the dimensionality, a layer-to-layer transfer
matrix can be constructed as a product of local vertex weights for infinitely
many points in the parameter space. Using this transfer matrix, the site
entropy is estimated numerically in the fully packed limit.Comment: 16pages, 4 eps figures, (v2) typos and Table 3 corrected. Refs added,
(v3) an error in an explanation of fig.2 corrected. Refs added. (v4) Changes
in the presentatio