Continued functions and Borel-Leroy transformation: Resummation of six-loop ε-expansions from different universality classes

Abstract

We handle divergent ε expansions in different universality classes derived from modified Landau-Wilson Hamiltonian. Landau-Wilson Hamiltonian can cater for describing critical phenomena on a wide range of physical systems which differ in symmetry conditions and the associated universality class. Numerically critical parameters are the most interesting physical quantities which characterize the singular behaviour around the critical point. More precise estimates are obtained for these critical parameters than previous predictions from Pade based methods and Borel with conformal mapping procedure. We use simple methods based on continued functions and Borel-Leroy transformation to achieve this. These accurate results are helpful in strengthening existing conclusions in different ϕ^4 models.

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Cited by in corpus (2)

• Extrapolation from hypergeometric functions, continued functions and Borel-Leroy transformation; Resummation of perturbative renormalization functions from field theories
• Convergence in divergent series related to perturbation methods using continued exponential and Shanks transformations