Exactly solvable heterophase fluctuations at a vibrational-entropy-driven first-order phase transition

We propose a new temperature-independent Hamiltonian that displays a vibrational-entropy-driven, first-order phase transition. Models of this kind do not presently exist in the statistical-mechanics literature, but are important in providing a simple realization of diffusionless, solid-to-solid martensitic transitions. The model employs anharmonic couplings between neighboring particles that cause the low-temperature phase to have a lower vibrational entropy (i.e., stiffer restoring forces) than the high-temperature phase. This entropy difference, as opposed to an internal energy difference, produces a sharp transition. In one dimension the model may be solved exactly using transfer-integral techniques, and the solutions show heterophase fluctuations connecting the parent and product phases only for temperatures very close to the transition. Consistent with this behavior, S(q,ω) found from molecular-dynamics simulations shows a central peak that is diffusive in origin.