Ising Model with a Scaling Interaction

A spin-infinity Ising model is presented in which there is a hierarchy of spin groupings, for which the interaction potential satisfies exactly the scaling hypothesis that group-group interactions involve only the group mean spin. The calculation of the critical exponents for this model is reduced to the solution of an eigenvalue problem which appears to be numerical tractable. The value of the critical exponent $\eta$ appears as a parameter of the model and formulas for the critical exponents $\delta$, $\gamma$, $\nu$ are presented. Assuming $\eta =0\mathrm{}$ for three dimensions, we obtain $\delta =5\mathrm{}$, $\gamma =1.30\mathrm{}$, and $\nu =0.65\mathrm{}$.