A recently proposed molecular model is discussed as a nontrivial extension of the Ising model. For $d=2\mathrm{}$ the two models are shown to be equivalent, while for $d>\mathrm{}2\mathrm{}$ 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 $d=3.\mathrm{}$ By finite size scaling the critical exponent has been found to be $\nu =0.44\mathrm{}\pm 0.02,$ thus establishing that the molecular model does not belong to the universality class of the Ising model for $d>\mathrm{}2.\mathrm{}$

• Received 24 May 2000

DOI:https://doi.org/10.1103/PhysRevE.62.6026