The exact spin Hamiltonian, induced by linear exchange coupling to a harmonic lattice with fixed periodic boundary conditions, is considered in the framework of renormalization-group recursion relations. Neglecting irrelevant variables, the Hamiltonian amounts to a replacement of the four-spin amplitude u0 by a(T-T1), with T1 proportional to the lattice compressibility. Hence the system exhibits a critical point with unrenormalized exponent values when Tc>Tt, but presumably a first-order transition for Tc<Tt, where TtfT1. The point Tc=Tt is expected to be a classical tricritical point. Experiments on NH4Cl are considered briefly.