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

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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 the next-to-next-to leading order chiral perturbation theory result in terms vanishing like 1/ℓ, for ℓ = Lt/L → ∞ and further showed that this deviation could be described by a correction to the rotator spectrum proportional to the square of the quadratic Casimir invariant. Here we confront this expectation with analytic nonperturbative results on the spectrum in 2 dimensions, by Balog and Hegedüs for n = 3, 4 and by Gromov, Kazakov and Vieira for n = 4, and find good agreement in both cases. We also consider the case of 3 dimensions.