Self-similar sequence transformation for critical exponents

Abstract

Self-similar sequence transformation is an original type of nonlinear sequence transformations allowing for defining effective limits of asymptotic sequences. The method of self-similar factor transformations is shown to be regular. This method is applied for calculating the critical exponents of the $O(N)$-symmetric $\varphi^4$ theory in three dimensions by summing asymptotic $\varepsilon$ expansions. It is shown that this method is straightforward and essentially simpler than other summation techniques involving complicated numerical calculations, while enjoying comparable accuracy.