In Theorem 1.4 (iii) of the original article, we stated that 1 $$\begin{aligned} \sqrt{N} (F_N - F(\beta )) \Rightarrow \mathcal {N}(0, \alpha _2) \end{aligned}$$ N ( F N - F ( β ) ) ⇒ N ( 0 , α 2 ) in the ferromagnetic regime $$J > 1$$ J > 1 and $$\beta > \frac{1}{2J}$$ β > 1 2 J . The proof was based on Theorem 1.5 (iii), which we proved in the paper, and a known random matrix theory result, given in the second part of (1.19) which reads 2 $$\begin{aligned} N^{1/2} \left( \mu _1 - \left( J + \frac{1}{J}\right) \right) \Rightarrow \mathcal {N}\left( 0, 2\left( 1- \frac{1}{J^2}\right) \right) \end{aligned}$$ N 1 / 2 μ 1 - J + 1 J ⇒ N 0 , 2 1 - 1 J 2 for $$J>1$$ J > 1 .