Criterion for DNA melting in the mean-field modified self-consistent phonon theory

We have examined the validity of the first-order-perturbation method in calculating eigenfunctions and the criterion for helix melting of mean-field polymers in the modified self-consistent phonon approach (MSPA) theory. It is found that the instability in the self-consistent solution is due to the breakdown of the first-order perturbation. The instability as a criterion for helix melting is therefore techniquely inappropriate. However, the breakdown of the perturbation is due to facts that are directly related to the onset of softening. Previously predicted melting temperatures for various sequence DNA polymers may still represent good estimates to the actual melting temperatures. An alternative criterion is required to define the melting temperature of the polymer DNA double helix in the MSPA theory.