Renormalized coupling constant in the Ising model

The three-dimensional Ising model is studied by means of the Swendsen-Wang, cluster, Monte Carlo method. The simulations are performed on finite sized systems up to the 96-cube, and the renormalized coupling constant is estimated to be g* = 25.0(5). We make further arguments and computations and say that g* greater than or equal to (g) over cap and 4.5 less than or similar to (g) over cap less than or similar to 5.4 so that g* > 0 which implies the validity of hyperscaling. The Josephson hyperscaling relation also appears to hold. We give estimates for some of the critical indices.