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

TL;DR

This paper develops an interpolation expansion method in fixed dimension to compute the non-trivial infrared fixed point of the three-dimensional scalar $ield^4$ theory, providing high-order series and resummation techniques to estimate critical exponents.

Contribution

It introduces a novel interpolation expansion approach for the 3D scalar fixed point and computes the critical exponent $ u$ to high order with multiple resummation methods.

Findings

Critical exponent $ u$ estimated as 0.6262(13).

High-order series computed up to order twenty five.

Multiple resummation techniques applied for accurate results.

Abstract

We compute the non--trivial infrared $\phi^4_3$--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 $\nu$.