Successive phase transitions and kink solutions in Φ⁸, Φ¹⁰, and Φ¹² field theories

Khare, Avinash; Christov, Ivan C.; Saxena, Avadh

doi:10.1103/PhysRevE.90.023208

Title: Successive phase transitions and kink solutions in Φ⁸, Φ¹⁰, and Φ¹² field theories

Journal Article · Wed Aug 27 00:00:00 EDT 2014 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

DOI:https://doi.org/10.1103/PhysRevE.90.023208· OSTI ID:1200676

Khare, Avinash ^[1]; Christov, Ivan C. ^[2]; Saxena, Avadh ^[2]

Indian Institute of Science Education and Research, Pune (India)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1200676

Alternate ID(s):: OSTI ID: 1180392

Report Number(s):: LA-UR-14-21202; PLEEE8

Journal Information:: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Vol. 90, Issue 2; ISSN 1539-3755

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 59 works

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References (32)

Kink-Antikink Collisions in the Two-Dimensional 4 Model Sugiyama, T. Progress of Theoretical Physics, Vol. 61, Issue 5 https://doi.org/10.1143/PTP.61.1550	journal	May 1979
Solitary waves and polynomial potentials Casahorran, J. Physics Letters A, Vol. 153, Issue 4-5 https://doi.org/10.1016/0375-9601(91)90794-9	journal	March 1991
Landau theory of domain walls for one-dimensional asymmetric potentials Sanati, Mahdi; Saxena, Avadh American Journal of Physics, Vol. 71, Issue 10 https://doi.org/10.1119/1.1578064	journal	October 2003
Crystallization of proteins accompanied by formation of a cylindrical surface Boulbitch, A. A. Physical Review E, Vol. 56, Issue 3 https://doi.org/10.1103/PhysRevE.56.3395	journal	September 1997
The Landau Theory of Phase Transitions Tolédano, J. C.; Tolédano, P. World Scientific Lecture Notes in Physics, Vol. 3 https://doi.org/10.1142/0215	book	August 1987
Kink interactions in the $(1 + 1)$ -dimensional $φ^{6}$ model Gani, Vakhid A.; Kudryavtsev, Alexander E.; Lizunova, Mariya A. Physical Review D, Vol. 89, Issue 12 https://doi.org/10.1103/PhysRevD.89.125009	journal	June 2014
Increased infall velocities in galaxy clusters from solitonic collisions? Castañeda Valle, David; Mielke, Eckehard W. Physical Review D, Vol. 89, Issue 4 https://doi.org/10.1103/PhysRevD.89.043504	journal	February 2014
Exact solutions of the Schrödinger equation for a class of anharmonic oscillators Leach, P. G. L. Physica D: Nonlinear Phenomena, Vol. 17, Issue 3 https://doi.org/10.1016/0167-2789(85)90216-7	journal	December 1985
Soliton structures in $P {(φ)}_{2}$ Lohe, M. A. Physical Review D, Vol. 20, Issue 12 https://doi.org/10.1103/PhysRevD.20.3120	journal	December 1979
Topological kinks in φ2n field theories: A variational approach Cooper, Fred; Simmons, L. M.; Sodano, Pasquale Physica D: Nonlinear Phenomena, Vol. 56, Issue 1 https://doi.org/10.1016/0167-2789(92)90051-N	journal	April 1992
Dynamics and statistical mechanics of a one-dimensional model Hamiltonian for structural phase transitions Krumhansl, J. A.; Schrieffer, J. R. Physical Review B, Vol. 11, Issue 9 https://doi.org/10.1103/PhysRevB.11.3535	journal	May 1975
Resonance structure in kink-antikink interactions in φ4 theory Campbell, David K.; Schonfeld, Jonathan F.; Wingate, Charles A. Physica D: Nonlinear Phenomena, Vol. 9, Issue 1-2 https://doi.org/10.1016/0167-2789(83)90289-0	journal	October 1983
General scalar bidimensional models including kinks Boya, Luis J.; Casahorran, Javier Annals of Physics, Vol. 196, Issue 2 https://doi.org/10.1016/0003-4916(89)90182-6	journal	December 1989
Structural phase transitions. II. Static critical behaviour Bruce, Alastair D. Advances in Physics, Vol. 29, Issue 1 https://doi.org/10.1080/00018738000101356	journal	February 1980
On the propagation of nonlinear acoustic waves in viscous and thermoviscous fluids Jordan, P. M.; Norton, G. V.; Chin-Bing, S. A. European Journal of Mechanics - B/Fluids, Vol. 34 https://doi.org/10.1016/j.euromechflu.2012.01.016	journal	July 2012
Half-kink lattice solution of the phi ⁶ model Sanati, M.; Saxena, A. Journal of Physics A: Mathematical and General, Vol. 32, Issue 23 https://doi.org/10.1088/0305-4470/32/23/309	journal	January 1999
Investigation of a class of one-dimensional nonlinear fields Gupta, Neelam; Sutherland, Bill Physical Review A, Vol. 14, Issue 5 https://doi.org/10.1103/PhysRevA.14.1790	journal	November 1976
Deformed defects for scalar fields with polynomial interactions Bazeia, D.; León, M. A. González; Losano, L. Physical Review D, Vol. 73, Issue 10 https://doi.org/10.1103/PhysRevD.73.105008	journal	May 2006
Classical φ6-field theory in (1+1) dimensions. A model for structural phase transitions Behera, S. N.; Khare, Avinash Pramana, Vol. 15, Issue 3 https://doi.org/10.1007/BF02847222	journal	September 1980
Statistical Mechanics of One-Dimensional Ginzburg-Landau Fields Scalapino, D. J.; Sears, M.; Ferrell, R. A. Physical Review B, Vol. 6, Issue 9 https://doi.org/10.1103/PhysRevB.6.3409	journal	November 1972
Solitary wave interactions in dispersive equations using Manton’s approach Kevrekidis, P. G.; Khare, Avinash; Saxena, A. Physical Review E, Vol. 70, Issue 5 https://doi.org/10.1103/PhysRevE.70.057603	journal	November 2004
Structure and phase transitions in antiphase boundaries of improper ferroelectrics Sonin, E. B.; Tagantsev, A. K. Ferroelectrics, Vol. 98, Issue 1 https://doi.org/10.1080/00150198908217590	journal	October 1989
On the ferroelastic phase transition of LiNH ₄ SO ₄ : a Brillouin scattering study and theoretical modelling Mroz, B.; Tuszynski, J. A.; Kiefte, H. Journal of Physics: Condensed Matter, Vol. 1, Issue 4 https://doi.org/10.1088/0953-8984/1/4/011	journal	January 1989
Topological Solitons Manton, Nicholas; Sutcliffe, Paul https://doi.org/10.1017/CBO9780511617034	book	January 2010
An effective Lagrangian for solitons Manton, N. S. Nuclear Physics B, Vol. 150 https://doi.org/10.1016/0550-3213(79)90309-2	journal	January 1979
One- and two-collective variable descriptions of two interacting sine-Gordon kinks Ferguson, C. D.; Willis, C. R. Physica D: Nonlinear Phenomena, Vol. 119, Issue 3-4 https://doi.org/10.1016/S0167-2789(98)00030-X	journal	August 1998
Monoclinic and triclinic phases in higher-order Devonshire theory Vanderbilt, David; Cohen, Morrel H. Physical Review B, Vol. 63, Issue 9 https://doi.org/10.1103/PhysRevB.63.094108	journal	January 2001
A model unified field equation Perring, J. K.; Skyrme, T. H. R. Nuclear Physics, Vol. 31 https://doi.org/10.1016/0029-5582(62)90774-5	journal	March 1962
Solitons in condensed matter: A paradigm Bishop, A. R.; Krumhansl, J. A.; Trullinger, S. E. Physica D: Nonlinear Phenomena, Vol. 1, Issue 1 https://doi.org/10.1016/0167-2789(80)90003-2	journal	April 1980
Physical dynamics of quasi-particles in nonlinear wave equations Christov, Ivan; Christov, C. I. Physics Letters A, Vol. 372, Issue 6 https://doi.org/10.1016/j.physleta.2007.08.038	journal	February 2008
Phenomenological theory of phase transitions in highly piezoelectric perovskites Sergienko, I. A.; Gufan, Yu. M.; Urazhdin, S. Physical Review B, Vol. 65, Issue 14 https://doi.org/10.1103/PhysRevB.65.144104	journal	March 2002
Solitary Wave Solutions of High Order Scalar Fields and Coupled Scalar Fields Yang, Jian-song; Lou, Sen-yue Zeitschrift für Naturforschung A, Vol. 54, Issue 3-4 https://doi.org/10.1515/zna-1999-3-407	journal	April 1999

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Zero rest mass soliton solutions Mohammadi, M.; Gheisari, R. Physica Scripta, Vol. 95, Issue 1 https://doi.org/10.1088/1402-4896/ab2c7b	journal	December 2019
Forces between kinks and antikinks with long-range tails Manton, N. S. Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 6 https://doi.org/10.1088/1751-8121/aaf9d1	journal	January 2019
Family of potentials with power law kink tails Khare, Avinash; Saxena, Avadh Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 36 https://doi.org/10.1088/1751-8121/ab30fd	journal	August 2019
Analytical study of kinklike structures with polynomial tails Bazeia, D.; Menezes, R.; Moreira, D. C. Journal of Physics Communications, Vol. 2, Issue 5 https://doi.org/10.1088/2399-6528/aac3cd	journal	May 2018
Kink-Kink and Kink-Antikink Interactions with Long-Range Tails Christov, Ivan C.; Decker, Robert J.; Demirkaya, A. Physical Review Letters, Vol. 122, Issue 17 https://doi.org/10.1103/physrevlett.122.171601	journal	May 2019
Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions Marjaneh, Aliakbar Moradi; Askari, Alidad; Saadatmand, Danial The European Physical Journal B, Vol. 91, Issue 1 https://doi.org/10.1140/epjb/e2017-80406-y	journal	January 2018
Scattering of the double sine-Gordon kinks Gani, Vakhid A.; Marjaneh, Aliakbar Moradi; Askari, Alidad The European Physical Journal C, Vol. 78, Issue 4 https://doi.org/10.1140/epjc/s10052-018-5813-1	journal	April 2018
Scattering of kinks of the sinh-deformed $$\varphi ^4$$ φ 4 model Bazeia, Dionisio; Belendryasova, Ekaterina; Gani, Vakhid A. The European Physical Journal C, Vol. 78, Issue 4 https://doi.org/10.1140/epjc/s10052-018-5815-z	journal	April 2018
Novel connection between lump-like structures and quantum mechanics Bazeia, D.; Losano, L.; Olmo, Gonzalo J. The European Physical Journal Plus, Vol. 133, Issue 7 https://doi.org/10.1140/epjp/i2018-12082-2	journal	July 2018
Scattering of the double sine-Gordon kinks Gani, Vakhid A.; Marjaneh, Aliakbar Moradi; Askari, Alidad arXiv https://doi.org/10.48550/arxiv.1711.01918	text	January 2017
Forces between Kinks and Antikinks with Long-range Tails Manton, N. S. arXiv https://doi.org/10.48550/arxiv.1810.03557	text	January 2018

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Title: Successive phase transitions and kink solutions in Φ⁸, Φ¹⁰, and Φ¹² field theories

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