LOW-TEMPERATURE EXPANSION OF THE GONIHEDRIC ISING-MODEL

We investigate a model of closed (d - 1)-dimensional soft-self-avoidin g random surfaces on a d-dimensional cubic lattice. The energy of a su rface configuration is given by E = J(n(2) + 4k n(4)), where n(2) is t he number of edges, where two plaquettes meet at a right angle and n(4 ) is the number of edges, where 4 plaquettes meet. This model can be r epresented as a Z(2)-spin system with ferromagnetic nearest-neighbour- , antiferromagnetic next-nearest-neighbour- and plaquette-interaction. It corresponds to a special case of a general class of spin systems i ntroduced by Wegner and Savvidy. Since there is no term proportional t o the surface area, the bare surface tension of the model vanishes, in contrast to the ordinary Ising model. By a suitable adaptation of Pei erls' 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 x(38) (x = e(-beta J)) sho ws that for k > 0 only the ferromagnetic low temperature phases remain stable. An analysis of low temperature expansions up to order x(44) f or the magnetization, susceptibility and specific heat in 3 dimensions yields critical exponents, which are in agreement with previous resul ts. (C) 1998 Elsevier Science B.V.