Study of spin-cell transformations for renormalization-group equations of spin systems

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Abstract
A study is made of the behavior of the spin correlation function for spin systems and lattice gases under spincell transformations in which the cell spin is chosen as a linear combination of the individual spins in the cells. It is found that the linear combination must satisfy certain conditions in order to give a satisfactory transformation; if too "unsymmetric" it will not yield convergence to a fixed point. We work in the context of the one-dimensional Gaussian and spherical models with long-range forces. For these models the critical indices can be found from our treatment since the connection between the interaction parameters and the spin correlation function is known. Although this explicit connection is lost in other models, our derivation includes certain general features that are independent of the underlying model and of dimensionality.