We formulate gauge-invariant Ising models in three dimension, which describe the open surface version of the Gonihedric Ising models. The energy of these open surfaces does not depend on their area but rather on the number of plaquettes meeting at right angles and the length of boundaries and "seams" where three plaquettes intersect. The models thus describe a gas of open surfaces with rigidity but no bare surface tension. Using mean field techniques, we obtain solutions to zero temperature phase diagram.
Keywords: Ising model, mean field theory, open surface solutions.
Journal of the National Science Foundation of Sri Lanka36 (4) 299-302