THE PHASE-DIAGRAM OF THE GONIHEDRIC 3D ISING-MODEL VIA CVM

We use the cluster variation method (CVM) to investigate the phase str ucture of the 3d gonihedric Ising actions defined by Savvidy and Wegne r. The geometrical spin cluster boundaries in these systems serve as m odels for the string worldsheets of the gonihedric string embedded in Z(3). The models are interesting from the statistical mechanical point of view because they have a vanishing bare surface tension. As a resu lt the action depends only on the angles of the discrete surface and n ot on the area, which is the antithesis of the standard 3d Ising model . The results obtained with the CVM are in good agreement with Monte C arlo simulations for the critical temperatures and the order of the tr ansition as the self-avoidance coupling kappa is varied. The value of the magnetization critical exponent beta = 0.062 +/- 0.003, calculated with the cluster variation-Pade approximant method, is also close to the simulation results.