Nontrivial extension of the two-dimensional ising model: the d-dimensional "molecular" model

A recently proposed molecular model is discussed as a nontrivial extension of the Ising model. For d=2 the two models are shown to be equivalent, while for d>2 the molecular model describes a peculiar second order transition from an isotropic high-temperature phase to a low-dimensional anisotropic low-temperature state. The general mean-field analysis is compared with the results achieved by a variational Migdal-Kadanoff real space renormalization group method and by standard Monte Carlo sampling for d=3. By finite size scaling the critical exponent has been found to be nu=0.44+/-0.02, thus establishing that the molecular model does not belong to the universality class of the Ising model for d>2.