Anomalous phase diagram of the elastic interface with non-local hydrodynamic interactions in the presence of quench disorder

TL;DR

This paper explores the complex phase behavior of elastic interfaces with non-local hydrodynamic interactions under quenched disorder, revealing multiple regimes and critical scaling features near depinning thresholds through numerical analysis.

Contribution

It introduces a comprehensive phase diagram for the quenched generalized elastic model, identifying three distinct dynamic regimes and analyzing critical behavior at depinning.

Findings

Identification of three distinct dynamic regimes in 1D disordered GEM.

Observation of second-order and first-order phase transitions depending on the velocity regime.

Numerical estimation of critical exponents near the depinning threshold.

Abstract

We investigate the influence of quenched disorder on the steady states of driven systems of the elastic interface with non-local hydrodynamic interactions. The generalized elastic model (GEM), which has been used to characterize numerous physical systems such as polymers, membranes, single-file systems, rough interfaces, and fluctuating surfaces, is a standard approach to studying the dynamics of elastic interfaces with non-local hydrodynamic interactions. The criticality and phase transition of the quenched generalized elastic model (qGEM) are investigated numerically, and the results are presented in a phase diagram spanned by two tuning parameters. We demonstrate that in 1-d disordered driven GEM, three qualitatively different behavior regimes are possible with a proper specification of the order parameter (mean velocity) for this system. In the vanishing order parameter regime, the steady-state order parameter approaches zero in the thermodynamic limit. A system with a non-zero mean velocity can be in either the continuous regime, which is characterized by a second-order phase transition, or the discontinuous regime, which is characterized by a first-order phase transition. The focus of this research was to investigate at the critical scaling features near the pinning-depinning threshold. The behavior of the quenched generalized elastic model at the critical depinning force is explored. Near the depinning threshold, the critical exponent obtained numerically.