Renormalized four-point coupling constant in the three-dimensional O(N) model with N → 0

We simulate self-avoiding walks on a cubic lattice and determine the second virial coefficient for walks of different lengths. This allows us to determine the critical value of the renormalized four-point coupling constant in the three-dimensional N-vector universality class for N = 0. We obtain g-bar*= 1.4005(5), where g-bar is normalized so that the three-dimensional field-theoretical β function behaves as β(g-bar) = -g-bar + g-bar2 for small g-bar. As a byproduct, we also obtain precise estimates of the interpenetration ratio Ψ*, Ψ* = 0.246 85(11) and of the exponent ν, ν = 0.5876(2). (fast track communication)