On Perturbation theory improved by Strong coupling expansion

Abstract

In theoretical physics, we sometimes have two perturbative expansions of physical quantity around different two points in parameter space. In terms of the two perturbative expansions, we introduce a new type of smooth interpolating function consistent with the both expansions, which includes the standard Padé approximant and fractional power of polynomial method constructed by Sen as special cases. We point out that we can construct enormous number of such interpolating functions in principle while the "best" approximation for the exact answer of the physical quantity should be unique among the interpolating functions. We propose a criterion to determine the "best" interpolating function, which is applicable except some situations even if we do not know the exact answer. It turns out that our criterion works for various examples including specific heat in two-dimensional Ising model, average plaquette in four-dimensional SU(3) pure Yang-Mills theory on lattice and free energy in c=1 string theory at self-dual radius. We also mention possible applications of the interpolating functions to system with phase transition.

arXiv comment31+11 pages, 15 figures, 9 tables, 1 Mathematica file; v3: minor corrections

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• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Interpolating between small- and large-$g$ expansions using Bayesian Model Mixing
• From weak to strong: constrained extrapolation of perturbation series with applications to dilute Fermi systems
• S-duality invariant perturbation theory improved by holography
• Self-similar interpolation in high-energy physics
• Monopoles, Clarified
• Prescription for choosing an interpolating function
• From Asymptotic Series to Self-Similar Approximants
• On interpolating anomalous dimension of twist-two operators with general spins