Manifold self-localization in a deformable medium

TL;DR

This paper investigates how directed manifolds in deformable media can become self-localized due to their own strain fields, revealing phase transitions influenced by temperature, dimensionality, and coupling strength.

Contribution

It introduces a theoretical framework describing self-localization phenomena of manifolds in deformable media, including phase transition behaviors.

Findings

Self-localization depends on temperature, dimensionality, and coupling strength.

Phase transitions between localized and free states can be continuous or discontinuous.

The model predicts conditions for the existence of self-localized manifold states.

Abstract

Directed manifolds (domain walls, interfaces, vortex lines) in a deformable medium can exist in a correlated state in which the manifold is self-localized by its own strain field. Depending on the temperature, manifold/medium dimensionalities, and the strength of the coupling with the medium, the degree of localization of the ground state can vary both continuously and discontinuously; there can be phase transitions from self- localized to the free-manifold state.