A minimal nonlinearity logarithmic potential: Kinks with super-exponential profiles

Abstract

We study a [Formula: see text]-dimensional field theory based on the [Formula: see text] potential which represents minimal nonlinearity in the context of phase transitions. There are three degenerate minima at [Formula: see text] and [Formula: see text]. There are novel, asymmetric kink solutions of the form [Formula: see text] connecting the minima at [Formula: see text] and [Formula: see text]. The domains with [Formula: see text] repel the linear excitations, the waves (e.g., phonons). Topology restricts the domain sequences and therefore the ordering of the domain walls. Collisions between domain walls are rich for properties such as transmission of kinks and particle conversion, etc. For illustrative purposes we provide a comparison of these results with the [Formula: see text] model and its half-kink solution, which has an exponential tail in contrast to the super-exponential tail for the [Formula: see text] potential. Finally, we place the results in the context of other logarithmic models.