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Title: 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 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 co-existence 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 quasi-exactly 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]
  1. Indian Institute of Science Education and Research, Pune (India)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
LA-UR-14-21202
Journal ID: ISSN 1539-3755; PLEEE8
Grant/Contract Number:
AC52-06NA25396
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)
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 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 co-existence 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 quasi-exactly 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}
}