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

Abstract

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 $1/\ell ,$ for $\ell =L_t/L\to \infty$ 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 $n=4$. We also consider the case of 3 dimensions.

25 pages, 1 figure

References in corpus (2)

• Massless sunset diagrams in finite asymmetric volumes
• Isospin susceptibility in the O($n$) sigma-model in the delta-regime

Cited by in corpus (3)

• Rotor Spectra and Berry Phases in the Chiral Limit of QCD on a Torus
• On the rotator Hamiltonian for the SU$(N)\times$SU$(N)$ sigma-model in the delta-regime
• High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice