Calculating critical temperature and critical exponents by self-similar approximants

Abstract

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 φ 4 field theory in three dimensions by summing asymptotic ε expansions. This method is shown to be essentially simpler than other summation techniques involving complicated numerical calculations, while enjoying comparable accuracy.