Convergent resummed linear delta expansion in the critical O(N) (\phi_i^2)^2_{3d} model

TL;DR

This paper applies an improved resummed linear delta expansion method to the critical O(N) phi^4 3D model, enhancing convergence and supporting Monte Carlo estimates for Bose-Einstein condensation temperature.

Contribution

It introduces an efficient resummation technique for the linear delta expansion, improving convergence for both large N and finite N=2 cases in the critical O(N) model.

Findings

Reproduces known large N results with high accuracy.

Supports recent Monte Carlo estimates for N=2 Bose-Einstein condensation.

Demonstrates accelerated convergence of the LDE method.

Abstract

The nonperturbative linear delta expansion (LDE) method is applied to the critical O(N) phi^4 three-dimensional field theory which has been widely used to study the critical temperature of condensation of dilute weakly interacting homogeneous Bose gases. We study the higher order convergence of the LDE as it is usually applied to this problem. We show how to improve both, the large-N and finite N=2, LDE results with an efficient resummation technique which accelerates convergence. In the large N limit, it reproduces the known exact result within numerical integration accuracy. In the finite N=2 case, our improved results support the recent numerical Monte Carlo estimates for the critical transition temperature of Bose-Einstein condensation.