Scaling of Energy Barriers for Flux Lines and Other Random Systems

TL;DR

This paper combines analytic and numerical methods to establish bounds on energy barriers for defect lines in random potentials, revealing they scale similarly to free energy fluctuations across various systems.

Contribution

It provides the first comprehensive bounds on energy barriers for flux lines and domain walls, showing their scaling behavior aligns with free energy fluctuations under broad conditions.

Findings

Energy barriers scale with free energy fluctuations

Bounds are applicable to multiple defect systems

Results hold for metastable to minimal energy configurations

Abstract

Using a combination of analytic arguments and numerical simulations, we determine lower and upper bounds for the energy barriers to the motion of a defect line in a random potential at low temperatures. We study the cases of magnetic flux lines in high-$T_{c}$ superconductors in 2 and 3 dimensions, and of domain walls in 2 dimensional random-field Ising models. The results show that, under fairly general conditions, energy barriers have the same scaling as the fluctuations in free energy, except for possible logarithmic factors. This holds not only for barriers between optimal configurations of the line, but also for barriers separating any metastable configuration from a configuration of minimal energy. Similar arguments may be applicable to other elastic media with impurities, such as bunches of flux lines.