Results from the 4PI Effective Action in 2- and 3-dimensions

TL;DR

This paper numerically solves the 4PI effective action equations for a symmetric scalar quartic theory in 2- and 3-dimensions, demonstrating convergence and comparing results with perturbation theory across different couplings.

Contribution

It provides a numerical lattice approach to solve 4PI equations in lower dimensions and analyzes the behavior of correlation functions at various couplings.

Findings

Good convergence for couplings less than 10 within 10 iterations

Results agree with perturbative calculations at small coupling

Deviations from perturbation theory at larger coupling

Abstract

We consider a symmetric scalar theory with quartic coupling and solve the equations of motion from the 4PI effective action in 2- and 3-dimensions using an iterative numerical lattice method. For coupling less than 10 (in dimensionless units) good convergence is obtained in less than 10 iterations. We use lattice size up to 16 in 2-dimensions and 10 in 3-dimensions and demonstrate the convergence of the results with increasing lattice size. The self-consistent solutions for the 2-point and 4-point functions agree well with the perturbative ones when the coupling is small and deviate when the coupling is large.