Successive phase transitions and kink solutions in ${\varphi }^8$, ${\varphi }^{10}$, and ${\varphi }^{12}$ field theories

Abstract

We obtain exact solutions for kinks in ${\varphi }^8$, ${\varphi }^{10}$ and ${\varphi }^{12}$ 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 ${\varphi }^4$ and ${\varphi }^6$ 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 ${\varphi }^{12}$ 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 ${\varphi }^{10}$ field theory, which is a quasi-exactly solvable (QES) model akin to ${\varphi }^6$, 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

References in corpus (3)

• Kink interactions in the (1+1)-dimensional ${\phi }^6$ model
• Deformed defects for scalar fields with polynomial interactions
• Physical dynamics of quasi-particles in nonlinear wave equations

Cited by in corpus (56)

• Kink-kink and kink-antikink interactions with long-range tails
• Long-range interactions of kinks
• Scattering of the ${\phi }^8$ kinks with power-law asymptotics
• Forces between Kinks and Antikinks with Long-range Tails
• Scattering of kinks of the sinh-deformed ${\phi }^4$ model
• Scattering of the double sine-Gordon kinks
• Kink-Antikink Collisions and Multi-Bounce Resonance Windows in Higher-Order Field Theories
• Kink Dynamics in a Parametric ${\varphi }^6$ System: A Model With Controllably Many Internal Modes
• High energy density in the collision of $N$ kinks in the ${\varphi }^4$ model
• Analytical study of kinklike structures with polynomial tails
• Interaction between kinks and antikinks with double long-range tails
• Kink-antikink scattering in the ${\varphi }^4$ model without static intersoliton forces
• Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions
• Explicit kinks in higher-order field theories
• Family of Potentials with Power-Law Kink Tails
• Collision of two kinks with inner structure
• Classical transitions with the topological number changing in the early Universe
• Kink-antikink collisions in the ${\varphi }^8$ model: short-range to long-range journey
• Kink-Antikink Collisions in the Periodic ${\phi }^4$ Model
• Deformations of Kink Tails
• Topological defects with power-law tails
• Kinks in higher-order polynomial models
• Exotic Final States in the ${\phi }^8$ Multi-Kink Collisions
• Kink solutions in logarithmic scalar field theory: Excitation spectra, scattering, and decay of bions
• A veritable zoology of successive phase transitions in the asymmetric $q$-voter model on multiplex networks
• Logarithmic Potential with Super-Super-Exponential Kink Profiles and Tails
• A new look at the double sine-Gordon kink-antikink scattering
• Wide Class of Logarithmic Potentials with Power-Tower Kink Tails
• Supersymmetric Inhomogeneous Field Theories in 1+1 Dimensions
• Quantum Corrections to Solitons in the ${\Phi }^8$ Model
• Collisions between kinks with long-range tails: a simple and efficient method
• Higher-order field theories: ${\varphi }^6$, ${\varphi }^8$ and beyond
• Explicit Kink Solutions in Several One-Parameter Family of Higher Order Field Theory Models
• Novel results for kinklike structures and their connections to quantum mechanics
• Novel connection between lump-like structures and quantum mechanics
• Four Decades of Kink Interactions in Nonlinear Klein-Gordon Models: A Crucial Typo, Recent Developments and the Challenges Ahead
• From Scalar Field Theories to Supersymmetric Quantum Mechanics
• Nonlinear waves in electromigration dispersion in a capillary
• Exact BPS double-kinks in generalized ${\varphi }^4$, ${\varphi }^6$ and sine-Gordon models
• Superposed Hyperbolic Kink and Pulse Solutions of Coupled ${\varphi }^4$, NLS and MKdV Equations
• The role of the massless phantom term in the stability of a non-topological soliton solution
• Stability Catalyzer for a Relativistic Non-Topological Soliton Solution
• Novel Deformation Function Creating or Destroying any Number of Even Kink Solutions
• A novel connection between scalar field theories and quantum mechanics
• From thin to thick domain walls: An example of the ${\phi }^8$ model
• Stability of solitary waves in nonlinear Klein-Gordon equations
• Bound States and Particle Production by Breather-Type Background Field Configurations
• Scattering of kinks in scalar-field models with higher-order self-interactions
• Faster-Than-Light Solitons in 1 + 1 Dimensions
• Introducing a Relativistic Nonlinear Field System With a Single Stable Non-Topological Soliton Solution in 1+1 Dimensions
• Kinks in buckled graphene uncompressed and compressed in the longitudinal direction
• Kink scattering in a Lorentz-violating ${\varphi }^6$ model
• Kink dynamics in a high-order field model
• Zero Rest Mass Soliton Solutions
• Kinks scattering in deformed ${\phi }^6$ model
• Remarks on sine-Gordon kink--fermion system: localized modes and scattering