Variational Resummation of $\epsilon$-Expansions of Critical Exponents of Nonlinear O(N)-Symmetric $\sigma$-Model in $2+\epsilon$ Dimensions

Abstract

We develop a method for extracting accurate critical exponents from perturbation expansions of the O(n)-symmetric nonlinear sigma-model in D=2+ epsilon dimensions. This is possible by considering the epsilon-expansions in this model as strong-coupling expansions of functions of the variable tildevarepsilon = 2(4-D)/(D-2), whose first five weak-coupling expansion coefficients of powers of tildevarepsilon are known from varepsilon-expansions of critical exponents in O(n)-symmetric phi^4-theory in D=4-epsilon dimensions.

Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re275

References in corpus (4)

• Seven-Loop Critical Exponents from Strong-Coupling phi^4-Theory in Three Dimensions
• Addendum to paper: Strong-Coupling Behavior of ${\varphi }^4$-Theories and Critical Exponents [Phys. Rev. D 57, 2264 (1998)]
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• Quantum Gravity in Large Dimensions
• Extrapolating the precision of the Hypergeometric Resummation to Strong couplings with application to the $\mathcal{P}\mathcal{T}-$Symmetric $i{\varphi }^3$ Field Theory