Scaling Theory of the Critical Region for Systems with Long-Range Forces

A scaling theory of the critical region is developed for systems with a pair potential $v\left(\overrightarrow{\mathrm{r}}\right)$ that falls off like a power of $\mathcal{r}$, the distance between particles, when $\mathcal{r}$ is large. The development, which leads to the same relations among critical exponents that weak-scaling theory predicts in the case of short-range forces, is associated with an appropriate generalization of Kadanoff's cell-site equations.