A generalization of the Ising model is solved, qualitatively, for its critical behavior. In the generalization the spin Sn--> at a lattice site n--> can take on any value from -∞ to ∞. The interaction contains a quartic term in order not to be pure Gaussian. The interaction is investigated by making a change of variable Sn-->=mψm(n)S'm, where the functions ψm(n-->) are localized wavepacket functions. There are a set of orthogonal wave-packet functions for each order-of-magnitude range of the momentum k-->. An effective interaction is defined by integrating out the wave-packet variables with momentum of order 1, leaving unintegrated the variables with momentum <0.5. Then the variables with momentum between 0.25 and 0.5 are integrated, etc. The integrals are computed qualitatively. The result is to give a recursion formula for a sequence of effective Landau-Ginsberg-type interactions. Solution of the recursion formula gives the following exponents: η=0, γ=1.22, ν=0.61 for three dimensions. In five dimensions or higher one gets η=0, γ=1, and ν=12, as in the Gaussian model (at least for a small quartic term). Small corrections neglected in the analysis may make changes (probably small) in the exponents for three dimensions.