Rice's ansatz for overdamped phi4 kinks at finite temperature.

High-speed kinks in a generalized discrete phi4 model.

We consider a generalized discrete phi4 model and demonstrate that it can support exact moving kink solutions in the form of tanh with an arbitrarily large velocity. The constructed exact moving solutions are dependent on the specific value of the propagation velocity. We demonstrate that in this class of models, given a specific velocity, the problem of finding the exact moving solution is int...

Statistical mechanics of kinks in 1+1 dimensions: Numerical simulations and double-Gaussian approximation.

We investigate the thermal equilibrium properties of kinks in a classical Φ4 field theory in 1+1 dimensions. From large scale Langevin simulations we identify the temperature below which a dilute gas description of kinks is valid. The standard dilute gas/WKB description is shown to be remarkably accurate below this temperature. At higher, “intermediate” temperatures, where kinks still exist, th...

Exact static solutions for discrete phi4 models free of the Peierls-Nabarro barrier: discretized first-integral approach.

We propose a generalization of the discrete Klein-Gordon models free of the Peierls-Nabarro barrier derived in Spreight [Nonlinearity 12, 1373 (1999)] and Barashenkov [Phys. Rev. E 72, 035602(R) (2005)], such that they support not only kinks but a one-parameter set of exact static solutions. These solutions can be obtained iteratively from a two-point nonlinear map whose role is played by the d...

Translationally invariant discrete kinks from one-dimensional maps.

For most discretizations of the phi4 theory, the stationary kink can only be centered either on a lattice site or midway between two adjacent sites. We search for exceptional discretizations that allow stationary kinks to be centered anywhere between the sites. We show that this translational invariance of the kink implies the existence of an underlying one-dimensional map phi(n+1) =F (phi(n)) ...

phi4 theory in 1+d dimensions at high temperature: Dimensional reduction.