Successive phase transitions and kink solutions in $Ï^{8}$, $Ï^{10}$, and $Ï^{12}$ field theories
arXiv:1402.6766 · doi:10.1103/PhysRevE.90.023208
Abstract
We obtain exact solutions for kinks in $Ï^{8}$, $Ï^{10}$ and $Ï^{12}$ field theories with degenerate minima, which can describe a second-order phase transition followed by a first-order one, a succession of two first-order phase transitions and a second-order phase transition followed by two first-order phase transitions, respectively. Such phase transitions are known to occur in ferroelastic and ferroelectric crystals and in meson physics. In particular, we find that the higher-order field theories have kink solutions with algebraically-decaying tails and also asymmetric cases with mixed exponential-algebraic tail decay, unlike the lower-order $Ï^4$ and $Ï^6$ theories. Additionally, we construct distinct kinks with equal energies in all three field theories considered, and we show the co-existence of up to three distinct kinks (for a $Ï^{12}$ potential with six degenerate minima). We also summarize phonon dispersion relations for these systems, showing that the higher-order field theories have specific cases in which only nonlinear phonons are allowed. For the $Ï^{10}$ field theory, which is a quasi-exactly solvable (QES) model akin to $Ï^6$, we are also able to obtain three analytical solutions for the classical free energy as well as the probability distribution function in the thermodynamic limit.
28 pages, 17 figures, REVTeX4.1 format; v3 corrects minor typos