Bound states of the $\phi^4$ model via the nonperturbative renormalization group

TL;DR

This paper investigates bound states in the scalar ^4 theory across dimensions 2 to 4 using the nonperturbative renormalization group, confirming a bound state in three dimensions with high accuracy.

Contribution

It applies the Blaizot--Me9ndez-Galain--Wschebor approximation within the nonperturbative RG to accurately analyze bound states in ^4 theory across various dimensions.

Findings

Confirmed the existence of a bound state in three dimensions

Mass of the bound state matches previous Monte-Carlo results within 1%

Extended analysis to all dimensions between two and four

Abstract

Using the nonperturbative renormalization group, we study the existence of bound states in the symmetry-broken phase of the scalar $\phi^4$ theory in all dimensions between two and four and as a function of the temperature. The accurate description of the momentum dependence of the two-point function, required to get the spectrum of the theory, is provided by means of the Blaizot--M\'endez-Galain--Wschebor approximation scheme. We confirm the existence of a bound state in dimension three, with a mass within 1% of previous Monte-Carlo and numerical diagonalization values.