A non trivial extension of the two-dimensional Ising model: the d-dimensional "molecular" model

Details A non trivial extension of the two-dimensional Ising model: the d-dimensional "molecular" model A non trivial extension of the two-dimensional Ising model: the d-dimensional "molecular" model

2000-05-24

arxiv.org/abs/cond-mat/0005413v1

Physics

Condensed Matter

Statistical Mechanics

25 pages, 5 figures

Scientific paper

10.1103/PhysRevE.62.6026

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 0.44\pm 0.02 thus establishing that the molecular model does not belong to the universality class of the Ising model for d>2.

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