Calculating critical temperature and critical exponents by self-similar approximants

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 $\varepsilon$ expansions. This method is shown to be essentially simpler than other summation techniques involving complicated numerical calculations, while enjoying comparable accuracy.

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