Pade-Borel approximation of the continuum limit of strong coupling lattice fields: Two-dimensional nonlinear O(N) sigma model at N ≥ 3

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