Critical Exponents for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-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 ${({\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\phi}}}^{2})}^{2}$ 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.