Reggeon field theory on a lattice

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 ${\sigma }_{\mathrm{tot}}\propto {\left(\ln s\right)}^{-\gamma }$ and ${\sigma }_{\mathrm{el}}\propto {\left(\ln s\right)}^{-2\mathrm{}\gamma -z}$. By studying the properties of the fixed point of an explicit nonlinear renormalization-group transformation on the lattice, we show that $-\gamma \le z\le 2$, so that both the Froissart bound and the constraint ${\sigma }_{\mathrm{el}}<{\sigma }_{\mathrm{tot}}$ are satisfied.