Critical renormalized coupling constants in the symmetric phase of the Ising models

Using a finite-size scaling method combined with extensive Monte Carlo measurements of high statistics, we calculate the four-, six- and eight-point renormalized coupling constants defined at zero momentum in the symmetric phase of the three-dimensional Ising system. The results of the 2D Ising system that are directly measured are also reported. Our value of the four-point coupling constant for the 3D system agrees very well with the available estimates from other methods. Our values of the six- and eight-point coupling constants are significantly different from those obtained by other methods for the 3D system, although they agree reasonably well in the 2D system. (author)