Critical Behavior of Magnets with Lattice Coupling

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 TₜT₁. The point Tc=Tₜ is expected to be a classical tricritical point. Experiments on NH₄Cl are considered briefly.