Critical Exponents for then-Vector Model in Three Dimensions from Field Theory

Abstract

We present a new calculation of the critical exponents of the $n$-vector model through field-theoretical methods. The coefficients of the renormalization functions of the ${\left({\overrightarrow{\varphi }}^2\right)}^2$ theory are expanded in powers of the coupling constant. Asymptotic estimates of large order of perturbation series are used to transform the divergent perturbation series into a convergent one. As a consequence, new and more precise values of critical exponents are obtained.