Spin-Spin Correlations in an Ising Model for Which Scaling is Exact

Abstract

In their recent work using the renormalization-group approach, Fisher, Ma, and Nickel derived results for $\eta$ when there is a long-range interaction, ${\mathcal{r}}^{-d-\sigma }$, which were seemingly at variance with the numerical results of Nagle and Bonner. The problem is the presence of nonthermodynamic terms in the spin-spin correlation function which never-theless contribute to the thermodynamics. We also find that the scaling relation between $\delta$ and $\eta$ fails to hold for $d>\mathrm{}2\mathrm{}\sigma$.