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

TL;DR

This paper introduces a variational resummation technique to accurately determine critical exponents from epsilon-expansions of the nonlinear O(N) sigma-model in dimensions close to two, bridging weak and strong coupling regimes.

Contribution

The authors develop a novel variational resummation method that leverages epsilon-expansions as strong-coupling expansions, improving the accuracy of critical exponent calculations in nonlinear sigma-models.

Findings

Enhanced accuracy in critical exponent estimation near two dimensions

Established a link between epsilon-expansions and strong-coupling functions

Demonstrated the method using known expansion coefficients

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.