Absence of the second-order phase transitions in the dimerized Ising chains with spin larger than 12

A general spin S Ising chain interacting with a single phonon mode of the harmonic lattice is studied. The thermodynamics of the spin system is calculated exactly for S = 1, $\text{1}\text{2}$ and $\text{3}\text{2}$, while self-consistent equations for the induced lattice distortions are derived. It is demonstrated that for S >$\text{1}\text{2}$ there is no second-order phase transition, in contrast to the case S = $\text{1}\text{2}$ which was proved to have a tricritical point. This is found to cohere with the previous studies of the dimerized magnetic model chains.