Low temperature expansion of the gonihedric Ising model Original Research Article

We investigate a model of closed (d - 1)-dimensional soft-self-avoiding random surfaces on a d-dimensional cubic lattice. The energy of a surface configuration is given by E = J(n2 + 4k n4), where n2 is the number of edges, where two plaquettes meet at a right angle and n4 is the number of edges, where 4 plaquettes meet. This model can be represented as a Z2-spin system with ferromagnetic nearest-neighbour, antiferromagnetic next-nearest-neighbour- and plaquetteinteraction. It corresponds to a special case of a general class of spin systems introduced by Wegner and Savvidy. Since there is no term proportional to the surface area, the bare surface tension of the model vanishes, in contrast to the ordinary Ising model. By a suitable adaptation of Peierlsʹ argument, we prove the existence of infinitely many ordered low temperature phases for the case k = 0. A low temperature expansion of the free energy in 3 dimensions up to order x38 (x = e−βJ) shows that for k > 0 only the ferromagnetic low temperature phases remain stable. An analysis of low temperature expansions up to order x44 for the magnetization, susceptibility and specific heat in 3 dimensions yields critical exponents, which are in agreement with previous results. © 1998 Elsevier Science B.V.