Statistical Mechanics of Double sinh-Gordon Kinks

Abstract

We study the classical thermodynamics of the double sinh-Gordon (DSHG) theory in 1+1 dimensions. This model theory has a double well potential, thus allowing for the existence of kinks and antikinks. Though it is nonintegrable, the DSHG model is remarkably amenable to analysis. Below we obtain exact single kink and kink lattice solutions as well as the asymptotic kink-antikink interaction. In the continuum limit, finding the classical partition function is equivalent to solving for the ground state of a Schrodinger-like equation obtained via the transfer integral method. For the DSHG model, this equation turns out to be quasi-exactly solvable. We exploit this property to obtain exact energy eigenvalues and wavefunctions for several temperatures both above and below the symmetry breaking transition temperature. The availability of exact results provides an excellent testing ground for large scale Langevin simulations. The probability distribution function (PDF) calculated from Langevin dynamics is found to be in striking agreement with the exact PDF obtained from the ground state wavefunction. This validation points to the utility of a PDF-based computation of thermodynamics utilizing Langevin methods. In addition to the PDF, field-field and field fluctuation correlation functions were computed and also found to be in excellent agreement with the exact results.

10 pages, 5 figures (embedded using epsfig), uses RevTeX plus macro (included). To appear in Physica D

References in corpus (1)

• Exact Thermodynamics of the Double sinh-Gordon Theory in 1+1-Dimensions

Cited by in corpus (12)

• Internal modes of a skyrmion in the ferromagnetic background in chiral magnets
• Geometry induced potential on a 2D-section of a wormhole: catenoid
• Semiclassical Particle Spectrum of Double Sine-Gordon Model
• Controlling One-Dimensional Langevin Dynamics on the Lattice
• Conditional quasi-exact solvability of the quantum planar pendulum and of its anti-isospectral hyperbolic counterpart
• Higher-order field theories: ${\varphi }^6$, ${\varphi }^8$ and beyond
• Explicit Kink Solutions in Several One-Parameter Family of Higher Order Field Theory Models
• Classical and quantum mechanics of a particle on a rotating loop
• Connections Between Complex PT-Invariant Solutions and Complex Periodic Solutions of Several Nonlinear Equations
• Phase transitions in quantum tunneling and quasi-exact solvability for a family of parametric double-well potentials
• Quantum-tunneling transitions and exact statistical mechanics of bistable systems with parametrized Dikandé-Kofané double-well potentials
• Statistical Mechanics of Lamé Solitons