Real-time dynamics of the O(N) model in 1+1 dimensions

We study the nonequilibrium dynamics of the O(N) model in classical and quantum field theory in 1+1 dimensions, for N>1. We compare numerical results obtained using the Hartree approximation and two next to leading order approximations: the bare vertex approximation and the two-particle irreducible 1/N expansion. The latter approximations differ through terms of order g2, where g is the scaled coupling constant, g=λ/N. In this paper we investigate the statement regarding the convergence with respect to g. The differences between these two approximation schemes are computed and found to be already small for relatively small values of N, when λ is fixed