Interpolation Parameter and Expansion for the Three Dimensional Non-Trivial Scalar Infrared Fixed Point

Abstract

We compute the non--trivial infrared ${\varphi }_3^4$--fixed point by means of an interpolation expansion in fixed dimension. The expansion is formulated for an infinitesimal momentum space renormalization group. We choose a coordinate representation for the fixed point interaction in derivative expansion, and compute its coordinates to high orders by means of computer algebra. We compute the series for the critical exponent $\nu$ up to order twenty five of interpolation expansion in this representation, and evaluate it using \pade, Borel--\pade, Borel--conformal--\pade, and Dlog--\pade resummation. The resummation returns $0.6262(13)$ as the value of $\nu$.

29 pages, Latex2e, 2 Postscript figures

References in corpus (2)

• Ising Universality in Three Dimensions: A Monte Carlo Study
• High temperature critical O(N) field models by LCE series