Non-Universality in Ising Models with Four Spin Interaction

We consider two bidimensional classical Ising models, coupled by a weak interaction bilinear in the energy densities of the two systems; the model contains, as limiting cases, the Ashkin–Teller and the Eight-vertex models for certain values of their parameters. We write the energy–energy correlations and the specific heat as Grassman integrals formally describing Dirac 1+1 dimensional interacting massive fermions on a lattice, and an expansion based on Renormalization Group is written for them, convergent up to temperatures very close to the critical temperature for small coupling. The asymptotic behaviour is determined by critical indices which are continuous functions of the coupling.