We construct an analog model of interacting Ising spins on a lattice which has the same critical behavior as Reggeon field theory, in the physical number of dimensions. At the critical point the total and elastic cross sections have asymptotic behaviors σtot∝(lns)-γ and σel∝(lns)-2γ-z. By studying the properties of the fixed point of an explicit nonlinear renormalization-group transformation on the lattice, we show that -γ≤z≤2, so that both the Froissart bound and the constraint σel<σtot are satisfied.