Flux lattice melting and depinning in the weakly frustrated 2D XY model

TL;DR

This study uses Monte Carlo simulations to explore phase transitions and vortex behaviors in the weakly frustrated 2D XY model, revealing new phases and the conditions under which phase coherence vanishes.

Contribution

It provides new insights into flux lattice melting and depinning phenomena in the weakly frustrated 2D XY model, including the discovery of a phase with orientational order but no phase coherence.

Findings

Single transition where phase coherence and vortex order vanish together for f=1/30

Existence of a phase with orientational order but no phase coherence for f=1/56

Helicity modulus vanishes at finite temperature for any finite frustration f

Abstract

Monte Carlo simulations of the frustrated 2D XY model were carried out at small commensurate values of the frustration $f$. For $f=1/30$ a single transition was observed at which phase coherence (finite helicity modulus) and vortex lattice orientational order vanish together. For $f=1/56$ a new phase in which phase coherence is absent but orientational order persists was observed. Where comparison is possible, the results are in detailed agreement with the behavior of the lattice Coulomb gas model of vortices. It is argued that the helicity modulus of the frustrated 2D XY model vanishes for any finite temperature in the limit of weak frustration $f$.