Bound states of the ${\varphi }^4$ model via the nonperturbative renormalization group

Using the nonperturbative renormalization group, we study the existence of bound states in the symmetry-broken phase of the scalar ${\varphi }^4$ 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.