Successive phase transitions and kink solutions in Φ⁸, Φ¹⁰, and Φ¹² field theories
Abstract
We obtain exact solutions for kinks in Φ8, Φ10, and Φ12 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 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 higher-order field theories have specific cases in which only nonlinear phonons are allowed. For the Φ10 field theory, which is a quasiexactly solvable 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:
-
- Indian Institute of Science Education and Research, Pune (India)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1200676
- Alternate Identifier(s):
- OSTI ID: 1180392
- Report Number(s):
- LA-UR-14-21202
Journal ID: ISSN 1539-3755; PLEEE8
- Grant/Contract Number:
- AC52-06NA25396
- Resource 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 1539-3755
- Publisher:
- American Physical Society (APS)
- 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
Citation Formats
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., 2014.
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. https://doi.org/10.1103/PhysRevE.90.023208
Khare, Avinash, Christov, Ivan C., and Saxena, Avadh. Wed .
"Successive phase transitions and kink solutions in Φ⁸, Φ¹⁰, and Φ¹² field theories". United States. https://doi.org/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 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 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 higher-order field theories have specific cases in which only nonlinear phonons are allowed. For the Φ10 field theory, which is a quasiexactly solvable 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 = {Wed Aug 27 00:00:00 EDT 2014},
month = {Wed Aug 27 00:00:00 EDT 2014}
}
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