Crystal growth models and Ising models. IV. Graphical solutions for correlations

Abstract

For pt.III see ibid., vol.11, p.555 (1978). Graphical expansions are used to obtain exact solutions for correlations in symmetric models of crystal growth disorder. These models are equivalent to Ising models with fields and competing multi-spin interactions constrained so as to give an effective reduction in dimensionality. The graphical solutions illustrate the importance of symmetry in these models and indicate the way in which an effective reduction in dimensionality occurs. It is shown that there are particular temperatures at which all correlations in a first-and-second-neighbour square lattice Ising model and certain correlations in an anisotropic FCC model can be obtained explicitly.