model is critical for $|\lambda| < 1$ (and non-critical otherwise), the quantity given above may be interpreted as a signature of criticality for this model. Unfortunately, the Berry phase *per spin*, $\varphi/M$, is not a physical quantity that is accessible via experiments. We can only measure the *total* Berry phase $\varphi$, which vanishes for all values of $\lambda$: i.e. $(1/M)\lim_{\gamma\rightarrow 0}\varphi = 0 \,(\text{mod } 2\pi),
\forall\lambda$. This is in agreement with Hamma [@Hamma], who also showed, via a different line of argument, that for a finite number of spins, the Berry phase acquired by the ground state is always trivial ($0$ or $2\pi$). As an alternative, it was suggested that the same quantity would be non-trivial in the thermodynamic limit: $\lim_{\gamma\rightarrow 0}\lim_{M
\rightarrow \infty}(\varphi/M) \neq 0$. However, for any physical, finite system, no matter how large, one is not able to detect criticality in this manner. In other words, any finite-size scaling behaviour is completely lacking, i.e. $\lim_{M \rightarrow
\infty}\lim_{\gamma\rightarrow 0}(\varphi/M) = 0\,\mbox{(mod
2$\pi$)}$; it is only in the thermodynamic limit itself that this method represents a signature of criticality, i.e. the limiting case is reached discontinuously. As such, the result’s worth is perhaps more of an abstract, mathematical 