Near-Equilibrium Dynamics of Crystalline Interfaces with Long-Range Interactions in 1+1 Dimensional Systems

TL;DR

This paper studies the dynamics of 1+1 dimensional crystalline interfaces with long-range interactions, revealing phase transitions and mobility behaviors near critical points, with implications for understanding interface roughening and pinning phenomena.

Contribution

It introduces a detailed analysis of interface dynamics with long-range interactions, highlighting phase transitions and deriving mobility expressions in both pure and disordered cases.

Findings

Mobility decreases to zero near the roughening transition without randomness.

A phase transition to a pinning phase occurs with substrate disorder.

Derived explicit expressions for non-linear response mobility.

Abstract

The dynamics of a one-dimensional crystalline interface model with long-range interactions is investigated. In the absence of randomness, the linear response mobility decreases to zero when the temperature approaches the roughening transition from above, in contrast to a finite jump at the critical point in the Kosterlitz-Thouless (KT) transition. In the presence of substrate disorder, there exists a phase transition into a low-temperature pinning phase with a continuously varying dynamic exponent $z>1$. The expressions for the non-linear response mobility of a crystalline interface in both cases are also derived.