Abstract
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 ${u}_{0}$ by $a(T\ensuremath{-}{T}_{1})$, with ${T}_{1}$ proportional to the lattice compressibility. Hence the system exhibits a critical point with unrenormalized exponent values when ${T}_{c}g{T}_{t}$, but presumably a first-order transition for ${T}_{c}l{T}_{t}$, where ${T}_{t}\ensuremath{\simeq}{T}_{1}$. The point ${T}_{c}={T}_{t}$ is expected to be a classical tricritical point. Experiments on N${\mathrm{H}}_{4}$Cl are considered briefly.
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