Successive phase transitions and kink solutions in Φ⁸, Φ¹⁰, and Φ¹² field theories
We obtain exact solutions for kinks in Φ⁸, Φ¹⁰, and Φ¹² field theories with degenerate minima, which can describe a secondorder phase transition followed by a firstorder one, a succession of two firstorder phase transitions and a secondorder phase transition followed by two firstorder 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 higherorder field theories have kink solutions with algebraicallydecaying tails and also asymmetric cases with mixed exponentialalgebraic tail decay, unlike the lowerorder Φ⁴ and Φ⁶ theories. Additionally, we construct distinct kinks with equal energies in all three field theories considered, and we show the coexistence of up to three distinct kinks (for a Φ¹² potential with six degenerate minima). We also summarize phonon dispersion relations for these systems, showing that the higherorder field theories have specific cases in which only nonlinear phonons are allowed. For the Φ¹⁰ field theory, which is a quasiexactly solvable (QES) model akin to Φ⁶, 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.
 Authors:

^{[1]};
^{[2]};
^{[2]}
 Indian Institute of Science Education and Research, Pune (India)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Report Number(s):
 LAUR1421202
Journal ID: ISSN 15393755; PLEEE8
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
 Additional Journal Information:
 Journal Volume: 90; Journal Issue: 2; Journal ID: ISSN 15393755
 Publisher:
 American Physical Society (APS)
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING; Mathematics; Mathematical Physics; Materials Science; High Energy Physics  Theory
 OSTI Identifier:
 1200676
 Alternate Identifier(s):
 OSTI ID: 1180392
Khare, Avinash, Christov, Ivan C., and Saxena, Avadh. Successive phase transitions and kink solutions in Φ⁸, Φ¹⁰, and Φ¹² field theories. United States: N. p.,
Web. doi:10.1103/PhysRevE.90.023208.
Khare, Avinash, Christov, Ivan C., & Saxena, Avadh. Successive phase transitions and kink solutions in Φ⁸, Φ¹⁰, and Φ¹² field theories. United States. doi:10.1103/PhysRevE.90.023208.
Khare, Avinash, Christov, Ivan C., and Saxena, Avadh. 2014.
"Successive phase transitions and kink solutions in Φ⁸, Φ¹⁰, and Φ¹² field theories". United States.
doi:10.1103/PhysRevE.90.023208. https://www.osti.gov/servlets/purl/1200676.
@article{osti_1200676,
title = {Successive phase transitions and kink solutions in Φ⁸, Φ¹⁰, and Φ¹² field theories},
author = {Khare, Avinash and Christov, Ivan C. and Saxena, Avadh},
abstractNote = {We obtain exact solutions for kinks in Φ⁸, Φ¹⁰, and Φ¹² field theories with degenerate minima, which can describe a secondorder phase transition followed by a firstorder one, a succession of two firstorder phase transitions and a secondorder phase transition followed by two firstorder 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 higherorder field theories have kink solutions with algebraicallydecaying tails and also asymmetric cases with mixed exponentialalgebraic tail decay, unlike the lowerorder Φ⁴ and Φ⁶ theories. Additionally, we construct distinct kinks with equal energies in all three field theories considered, and we show the coexistence of up to three distinct kinks (for a Φ¹² potential with six degenerate minima). We also summarize phonon dispersion relations for these systems, showing that the higherorder field theories have specific cases in which only nonlinear phonons are allowed. For the Φ¹⁰ field theory, which is a quasiexactly solvable (QES) model akin to Φ⁶, 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.},
doi = {10.1103/PhysRevE.90.023208},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},
number = 2,
volume = 90,
place = {United States},
year = {2014},
month = {8}
}