Abstract
We analyze a statistical system with an energy functional which is proportional to the linear size of the surfaces. We find a dual system, whose high temperature expansion generates random surfaces with a linear amplitude. In this model the independent variable is placed at the vertices of the 3D cubic lattice and takes four values. The interaction is nearest neighbour and anisotropic. These dual systems have the same relation to each other as the 3D Ising ferromagnet has to the 3D gauge spin system.
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