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* = 1.4005( 5), where g is normalized so that the three-dimensional field-theoretical beta function behaves as beta(g) = -g + g(2) for small g. As a byproduct, we also obtain precise estimates of the interpenetration ratio psi*, psi* = 0.246 85( 11) and of the exponent v, v = 0.5876( 2).