A non trivial extension of the two - dimensional Ising model : the d - dimensional “ molecular ” model . Fabio

A recently proposed molecular model is discussed as a non-trivial 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 ν = 0.44 ± 0.02 thus establishing that the molecular model does not belong to the universality class of the Ising model for d > 2. PACS numbers: 64.60.Cn, 64.60.Fr, 62.50.+p, 05.50.+q Typeset using REVTEX 1