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In a previous paper we found that the isospin susceptibility of the O($n$)sigma-model calculated in the standard rotator approximation differs from thenext-to-next to leading order chiral perturbation theory result in termsvanishing like $1/\ell\,,$ for $\ell=L_t/L\to\infty$ and further showed thatthis deviation could be described by a correction to the rotator spectrumproportional to the square of the quadratic Casimir invariant. Here we confrontthis expectation with analytic nonperturbative results on the spectrum in 2dimensions, by Balog and Heged\"us for $n=3,4$ and by Gromov, Kazakov andVieira for $n=4$. We also consider the case of 3 dimensions.

Casimir squared correction to the standard rotator Hamiltonian for the O($n$) sigma-model in the delta-regime