 Solution

If the singular free-energy density is set by one correlated region, then $f_s\sim {\xi }^{-d}$. With reduced temperature $t$, the definitions $\xi \sim |t{|}^{-\nu }$ and $f_s\sim |t{|}^{2-\alpha }$ therefore giveThis is the hyperscaling relation; it assumes that no dangerously irrelevant coupling introduces an additional scale.