Pade-Borel approximation of the continuum limit of strong coupling lattice fields: Two dimensional non-linear O(N) sigma model at N>=3

Details Pade-Borel approximation of the continuum limit of strong coupling lattice fields: Two dimensional non-linear O(N) sigma model at N>=3 Pade-Borel approximation of the continuum limit of strong coupling lattice fields: Two dimensional non-linear O(N) sigma model at N>=3

2011-11-24

arxiv.org/abs/1111.5804v1

Physical Review D84, 105025 (2011)

Physics

High Energy Physics

High Energy Physics - Lattice

7 pages, 4 figures

Scientific paper

10.1103/PhysRevD.84.105025

Based on the strong coupling expansion, we reinvestigate 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 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 non-perturbative mass gap at N>=3 and find the agreement with the exact result by Hasenfratz et.al.

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