Padé-Borel approximation of the continuum limit of strong coupling lattice fields: Two-dimensional nonlinearO(N)sigma model atN≥3

Abstract

Based on the strong coupling expansion, we reinvestigate the two-dimensional $O(N)$ sigma model by the use of Pad\'e-Borel approximants. The conventional strong coupling expansion of the mass square $M$ in momentum space in $\ensuremath{\beta}=1/{g}^{2}$ is inverted to give $\ensuremath{\beta}$ expanded in $1/M$. Borel transform of $\ensuremath{\beta}$ with respect to $M$ is carried out and the result is improved as the rational function by the Pad\'e method. We find the behavior of Pad\'e-Borel transformed bare coupling at 18th order is consistent for $N\ensuremath{\ge}3$ with that of continuum scaling to the four-loop perturbation theory. We estimate the nonperturbative mass gap at $N\ensuremath{\ge}3$ and find agreement with the exact result by Hasenfratz et. al.