FAST TRACK COMMUNICATION: 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 \bar{g}^* = 1.4005(5) , where \bar{g} is normalized so that the three-dimensional field-theoretical β function behaves as \beta(\bar{g}) = - \bar{g} + \bar{g}^2 for small \bar{g} . 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).