Constraint effective potential in O(4) Φ4 theory

We present a numerical determination of parameters of the constraint effective potential in the O(4) non-linear σ-model in 4 dimensions. We determine the infinite volume value of the analog of the pion decay constant F from the minimum of the effective potential, and the σ-mass from the second derivative of the effective potential at the minimum. The extrapolation of these quantities to infinite volume is based on chiral perturbation theory in combination with perturbation theory in the renormalized quartic coupling. For the first time we observe the divergence of the susceptibility of the length of the mean field proportional to the logarithm of the linear size of the lattice, which is caused by the two-pion cut of the theory. The form of the divergence determines the σ-mass, or alternatively the renormalized quartic coupling, using one loop renormalized perturbation theory. The resulting values of the renormalized quartic coupling agree very well with the work of Luescher and Weisz. Using a nonlocal cluster algorithm we obtain high precision of our numerical data. (orig.)