The ordered phase of Reggeon field theory is analyzed in the framework of the Reggeon quantum spin model with three- and four-point couplings. We work at a particular value of the bare-intercept gap, ${\Delta }_0={\Delta }_{0M}$, for which the spin model is exactly solvable in one transverse dimension. We include the higher single-site states by developing a perturbative expansion for this spin model. The expansion is shown to be characterized by a small dimensionless parameter $\epsilon =\frac{16{\alpha }_0^{\prime }{{\Delta }_{0M}}^3}{{r_0}^4}$. At each stage of calculation we are able to relate the spin model to the continuum Reggeon field theory by letting the lattice spacing go to zero. The two-point function is then calculated to order $\epsilon$. We find that the necessary condition for satisfying Reggeon unitarity, of Regge-Mandelstam singularities appearing in the complex angular momentum plane, is satisfied in the form of the two-Reggeon cut.

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