Calculating critical temperature and critical exponents by self-similar approximants

Abstract

Self-similar approximation theory allows for defining effective sums of asymptotic series. The method of self-similar factor approximants is applied for calculating the critical temperature and critical exponents of the $O(N)$-symmetric ${\phi }^4$ field theory in three dimensions by summing asymptotic $\epsilon$ expansions. This method is shown to be essentially simpler than other summation techniques involving complicated numerical calculations, while enjoying comparable accuracy.

Comments: Latex file, 14 pages. arXiv admin note: substantial text overlap with arXiv:2201.10806